Find the value of 'a' if X+a is a factor (zero) of the polynomial 2x²+2ax+5x+10.

3

(a)

If zeros of the polynomial x²+(a+1)x+b are 2 and -3, then find the value of (a+b).

3

(a)

Find the zeros of the quadratic polynomial x² +7x+10 and verify relationship between the zeros and the coefficients.

3

(a)

Find a quadratic polynomial whose one zero is 7 and sum of zeroes is -18.

3

(a)

If a and β are the zeroes of the quadratic polynomial p(x)=ax²+bx+c, then evaluate a²β+aβ² .

3

(a)

If a and β are the zeroes of the quadratic polynomial f(x)=ax^2+bx+c, then find the difference between the zeroes.
\(\left( \alpha -\beta \right) ^{ 2 }=\left( \alpha +\beta \right) ^{ 2 }-4\alpha \beta \quad or\quad \left( \alpha -\beta \right) =\pm \sqrt { \left( \alpha +\beta \right) ^{ 2 }-4\alpha \beta } \)

3

(a)

Can the quadratic polynomial x²+kx+k have equal zeroes for some odd integer k>1?

3

(a)

If 2 and -3 are the zeroes of the quadratic polynomial x²+(a+1)x+b, then find the values of a and b.

3

(a)

It is given that 1 is one of the zeroes of the polynomial 7x-x³-6. Find its other zeroes.

3

(a)

Given that, x²+2x-3 is a factor of f(x)=x⁴+6x³+2a^x2+bx-3a. Find the values of a and b.

3

(a)

Find the zeroes of polynomial \(4\sqrt { 3x^{ 2 } } +5x-22\sqrt { 3 } \) and verify the relation between the zeroes and coefficient of the polynomial.

3

(a)

Divide x⁴-3x²+4x+5 by x²-x+1 and find its quotient and remainder.

3

(a)

If α and β are zeroes of the polynomial 21y²-y-2, then find a quadratic polynomial, whose zeroes 2α and 2β.

3

(a)

If the sum of the zeroes of the polynomial p(x)=(a+1)x²+(2a+3)x+(3a+4) is -1, then find the product of its zeroes.

3

(a)

For which values of a and b, the zeroes of q(x)=x³+2x²+a are also the zeroes of the polynomial p(x)=x⁵-x⁴-4x³+3x²+3x+b?

3

(a)