Polynomials - Class 10 CBSE | Mathematics

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Polynomials - Class 10 CBSE

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10th grade

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Slide 1
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Polynomials - Class 10 CBSE

by
Salman Nizarudin
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Question 2
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Q.
If the sum of zeroes of the quadratic polynomial $3x^2-kx+6$ is 3, then find the value of k. (2012)

answer
9
9
alternatives
answer explanation
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Question 3
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Q.
If α and β are the zeroes of the polynomial $ax^2+bx+c$ , find the value of $\alpha^2+\beta^2$ . (2013)

answer choices
$\frac{b^2-2ac}{a^2}$
$\frac{b^2-2ac}{a^2}$
$\frac{a^2-2ac}{b^2}$
$\frac{a^2+2ac}{b^2}$
 <math><semantics><mrow><mfrac><mrow><msup><mi>b</mi><mn>2</mn></msup><mo>−</mo><mn>2</mn><mi>a</mi><mi>c</mi></mrow><msup><mi>a</mi><mn>2</mn></msup></mfrac></mrow><annotation encoding="application/x-tex">\frac{b^2-2ac}{a^2}</annotation></semantics></math>a2b2−2ac 
alternatives
 <math><semantics><annotation encoding="application/x-tex">\frac{b^2-2ac}{a^2}</annotation></semantics></math>a2b2−2ac 
 <math><semantics><mrow><mfrac><mrow><msup><mi>a</mi><mn>2</mn></msup><mo>−</mo><mn>2</mn><mi>a</mi><mi>c</mi></mrow><msup><mi>b</mi><mn>2</mn></msup></mfrac></mrow><annotation encoding="application/x-tex">\frac{a^2-2ac}{b^2}</annotation></semantics></math>b2a2−2ac 
 <math><semantics><mrow><mfrac><mrow><msup><mi>a</mi><mn>2</mn></msup><mo>+</mo><mn>2</mn><mi>a</mi><mi>c</mi></mrow><msup><mi>b</mi><mn>2</mn></msup></mfrac></mrow><annotation encoding="application/x-tex">\frac{a^2+2ac}{b^2}</annotation></semantics></math>b2a2+2ac 
answer explanation
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Question 4
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Q.
Form a quadratic polynomial whose zeroes are 3 + √2 and 3 – √2. (2012)
answer choices
$x^2+6x+7$
$x^2-6x-7$
$x^2-6x+7$
$x^2-7x+6$
 <math><semantics><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>6</mn><mi>x</mi><mo>+</mo><mn>7</mn></mrow><annotation encoding="application/x-tex">x^2+6x+7</annotation></semantics></math>x2+6x+7 
alternatives
 <math><semantics><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>−</mo><mn>6</mn><mi>x</mi><mo>−</mo><mn>7</mn></mrow><annotation encoding="application/x-tex">x^2-6x-7</annotation></semantics></math>x2−6x−7 
 <math><semantics><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>−</mo><mn>6</mn><mi>x</mi><mo>+</mo><mn>7</mn></mrow><annotation encoding="application/x-tex">x^2-6x+7</annotation></semantics></math>x2−6x+7 
 <math><semantics><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>−</mo><mn>7</mn><mi>x</mi><mo>+</mo><mn>6</mn></mrow><annotation encoding="application/x-tex">x^2-7x+6</annotation></semantics></math>x2−7x+6 
answer explanation
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Question 5
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If the zeroes of the polynomial $x^2+px+q$ are double in value to the zeroes of $2x^2-5x-3$ , find the value of p and q. (2012)

answer choices
p = -3, q = -2
p = 3, q = 2
p = 5, q = 6
p = -5, q = -6
p = -3, q = -2
alternatives
p = 3, q = 2
p = 5, q = 6
p = -5, q = -6
answer explanation
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Question 6
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Q.
If α and β are the zeroes of the polynomial $6y^2-7y+2$ , find a quadratic polynomial whose zeroes are $\frac{1}{\alpha}$ and $\frac{1}{\beta}$ . (2012)
answer choices
$2x^2-7x+6$
$\frac{1}{2}\left(2x^2-7x+6\right)$
$\frac{1}{2}\left(2x^2+7x-6\right)$
$2x^2-7x-6$
 <math><semantics><mrow><mn>2</mn><msup><mi>x</mi><mn>2</mn></msup><mo>−</mo><mn>7</mn><mi>x</mi><mo>+</mo><mn>6</mn></mrow><annotation encoding="application/x-tex">2x^2-7x+6</annotation></semantics></math>2x2−7x+6 
alternatives
 <math><semantics><annotation encoding="application/x-tex">\frac{1}{2}\left(2x^2-7x+6\right)</annotation></semantics></math>21(2x2−7x+6) 
 <math><semantics><mrow><mfrac><mn>1</mn><mn>2</mn></mfrac><mrow><mo fence="true">(</mo><mn>2</mn><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>7</mn><mi>x</mi><mo>−</mo><mn>6</mn><mo fence="true">)</mo></mrow></mrow><annotation encoding="application/x-tex">\frac{1}{2}\left(2x^2+7x-6\right)</annotation></semantics></math>21(2x2+7x−6) 
 <math><semantics><mrow><mn>2</mn><msup><mi>x</mi><mn>2</mn></msup><mo>−</mo><mn>7</mn><mi>x</mi><mo>−</mo><mn>6</mn></mrow><annotation encoding="application/x-tex">2x^2-7x-6</annotation></semantics></math>2x2−7x−6 
answer explanation
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Question 7
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Q.
Given that x – √5 is a factor of the polynomial $x^3-3\sqrt{5}x^2-5x+15\sqrt{5}$ , find all the zeroes of the polynomial. (2012, 2016)
answer choices
-√5, √5 and 3√5
-√5, 2√5 and 3√5
-√5, 2√5 and -3√5
-√5, 4√5 and -3√5
-√5, √5 and 3√5
alternatives
-√5, 2√5 and 3√5
-√5, 2√5 and -3√5
-√5, 4√5 and -3√5
answer explanation
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Question 8
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Q.
If p(x) = $x^3-2x^2+kx+5$ is divided by (x – 2), the remainder is 11. Find k. Hence find all the zeroes of $x^3+kx^2+3x+1$ . (2012)
answer choices
k=4, zeroes = 1, 1, 1
k=-6, zeroes = 1, 1, 1
k=3, zeroes = -1, -1, -1
k=-6, zeroes = -1, -1, -1
k=4, zeroes = 1, 1, 1
alternatives
k=-6, zeroes = 1, 1, 1
k=3, zeroes = -1, -1, -1
k=-6, zeroes = -1, -1, -1
answer explanation
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Question 9
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Q.
If α and β are zeroes of p(x) = $kx^2+4x+4$ , such that $\alpha^2+\beta^2=24$ , find k. (2013)
answer choices
$k=1\ ,\ -\frac{2}{3}$
$k=-1\ ,\ \frac{2}{3}$
$k=-2\ ,\ \frac{1}{3}$
$k=2\ ,\ -\frac{1}{3}$
 <math><semantics><mrow><mi>k</mi><mo>=</mo><mn>1</mn><mtext> </mtext><mo separator="true">,</mo><mtext> </mtext><mo>−</mo><mfrac><mn>2</mn><mn>3</mn></mfrac></mrow><annotation encoding="application/x-tex">k=1\ ,\ -\frac{2}{3}</annotation></semantics></math>k=1 , −32 
alternatives
 <math><semantics><mrow><mi>k</mi><mo>=</mo><mo>−</mo><mn>1</mn><mtext> </mtext><mo separator="true">,</mo><mtext> </mtext><mfrac><mn>2</mn><mn>3</mn></mfrac></mrow><annotation encoding="application/x-tex">k=-1\ ,\ \frac{2}{3}</annotation></semantics></math>k=−1 , 32 
 <math><semantics><mrow><mi>k</mi><mo>=</mo><mo>−</mo><mn>2</mn><mtext> </mtext><mo separator="true">,</mo><mtext> </mtext><mfrac><mn>1</mn><mn>3</mn></mfrac></mrow><annotation encoding="application/x-tex">k=-2\ ,\ \frac{1}{3}</annotation></semantics></math>k=−2 , 31 
 <math><semantics><mrow><mi>k</mi><mo>=</mo><mn>2</mn><mtext> </mtext><mo separator="true">,</mo><mtext> </mtext><mo>−</mo><mfrac><mn>1</mn><mn>3</mn></mfrac></mrow><annotation encoding="application/x-tex">k=2\ ,\ -\frac{1}{3}</annotation></semantics></math>k=2 , −31 
answer explanation
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Question 10
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Q.
If the polynomial $\left(x^4+2x^3+8x^2+12x+18\right)$ is divided by another polynomial $\left(x^2+5\right)$ , the remainder comes out to be (px + q), find the values of p and q.

answer choices
p = -2 and q = -3
p = 3 and q = 2
p = -3 and q = -2
p = 2 and q = 3
p = -2 and q = -3
alternatives
p = 3 and q = 2
p = -3 and q = -2
p = 2 and q = 3
answer explanation
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Question 11
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Q.
On dividing $3x^3+4x^2+5x-13$ by a polynomial g(x) the quotient and remainder were 3x +10 and 16x – 43 respectively. Find the polynomial g(x). (2017 OD)

answer choices
$x^2-2x+3$
$x^2-3x+2$
$x^2-2x+2$
$x^2-2x-2$
 <math><semantics><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>−</mo><mn>2</mn><mi>x</mi><mo>+</mo><mn>3</mn></mrow><annotation encoding="application/x-tex">x^2-2x+3</annotation></semantics></math>x2−2x+3 
alternatives
 <math><semantics><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>−</mo><mn>3</mn><mi>x</mi><mo>+</mo><mn>2</mn></mrow><annotation encoding="application/x-tex">x^2-3x+2</annotation></semantics></math>x2−3x+2 
 <math><semantics><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>−</mo><mn>2</mn><mi>x</mi><mo>+</mo><mn>2</mn></mrow><annotation encoding="application/x-tex">x^2-2x+2</annotation></semantics></math>x2−2x+2 
 <math><semantics><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>−</mo><mn>2</mn><mi>x</mi><mo>−</mo><mn>2</mn></mrow><annotation encoding="application/x-tex">x^2-2x-2</annotation></semantics></math>x2−2x−2 
answer explanation
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