If 1 is a zero of the polynomial p(x) = ax² – 3(a – 1) x – 1, then find the value of a.

If α and β are zeroes of the quadratic polynomial x² – 6x + a; find the value of ‘a’ if 3α + 2β = 20.

Using division algorithm, find the quotient on dividing f(x) by g(x), where f(x) = 6x³ + 13x² + x – 2 and g(x) = 2x + 1

Find all the zeroes of  $x^4-3x^3+6x-4$  , if two of its zeroes are 
 $\sqrt{2}\ and-\sqrt{2}$  

If one zero of the polynomial (a² + 9) x² + 13x + 6a is reciprocal of the other, find the value of ‘a’.

What is the number of zeroes of the polynomial y = p(x)?

If the zeroes of the quadratic polynomial x² + bx + c , c ≠ 0are equal, then

The number of polynomials having zeroes as –2 and 5 is

The degree of the polynomial (x + 1)(x² – x – x⁴ +1) is:

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

Given that one of the zeroes of the cubic polynomial ax³ + bx² + cx + d is zero, the product of the other two zeroes is

If one of the zeroes of the quadratic polynomial (k – 1)x² + kx + 1 is –3, then the value of k is

If sum of the squares of zeroes of the quadratic polynomial 6x² + x + k is 25/36, the value of k is:

If (x + 1) is a factor of x²− 3ax +3a − 7, then the value of a is: