Polynomials - Class 10 CBSE

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

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

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)

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)

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)

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)

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

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.