Polynomials - Class 10 CBSE

Polynomials - Class 10 CBSE

by

Salman Nizarudin

Multiple Choice

If α and β are the zeroes of the polynomial  $ax^2+bx+c$  , find the value of  $\alpha^2+\beta^2$  . (2013)

•  $\frac{b^2-2ac}{a^2}$  

•  $\frac{b^2-2ac}{a^2}$  

•  $\frac{a^2-2ac}{b^2}$  

•  $\frac{a^2+2ac}{b^2}$  

Multiple Choice

Form a quadratic polynomial whose zeroes are 3 + √2 and 3 – √2. (2012)

• $x^2+6x+7$
  

• $x^2-6x-7$

• $x^2-6x+7$

• $x^2-7x+6$

Multiple Choice

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)

• p = -3, q = -2

• p = 3, q = 2

• p = 5, q = 6

• p = -5, q = -6

Multiple Choice

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)

•  $2x^2-7x+6$  

•  $\frac{1}{2}\left(2x^2-7x+6\right)$  

•  $\frac{1}{2}\left(2x^2+7x-6\right)$  

•  $2x^2-7x-6$  

Multiple Choice

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)

• -√5, √5 and 3√5

• -√5, 2√5 and 3√5

• -√5, 2√5 and -3√5

• -√5, 4√5 and -3√5

Multiple Choice

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)

• k=4, zeroes = 1, 1, 1

• k=-6, zeroes = 1, 1, 1

• k=3, zeroes = -1, -1, -1

• k=-6, zeroes = -1, -1, -1

Multiple Choice

If α and β are zeroes of p(x) =  $kx^2+4x+4$ , such that  $\alpha^2+\beta^2=24$ , find k. (2013)

•  $k=1\ ,\ -\frac{2}{3}$  

•  $k=-1\ ,\ \frac{2}{3}$  

•  $k=-2\ ,\ \frac{1}{3}$  

•  $k=2\ ,\ -\frac{1}{3}$  

Multiple Choice

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.

• p = -2 and q = -3

• p = 3 and q = 2

• p = -3 and q = -2

• p = 2 and q = 3

Multiple Choice

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)

•  $x^2-2x+3$  

•  $x^2-3x+2$  

•  $x^2-2x+2$  

•  $x^2-2x-2$