If the polynomial `7x^(3)+ax+b` is divisible by `x^(2)-x+1`, find the value of `2a+b.`

If 0 and 1 are the zeroes of the polynomial f (x) = 2x ^(3) - 3x ^(2) + ax +b, then find the values of a and b.

If 2 is a zero of the polynomial p (x) = 2x ^(2) - 3x + 7a, then find the value of a.

If alpha" and "beta are the zeroes of the polynomial p(x)= 3x^(2)-14x+15 , find the value of alpha^(2)+beta^(2) .

If the product of the zeroes of the polynomial p(x)= ax^(2)+11x+12 is 6, find the value of a.

If tanx=b/a , find the value of (acos2x+bsin2x) .

When the polynomial p(x)= x^(3)+2x^(2)+kx+3 is divided by x-3 , the remainder is 21. Find the value of k and the quotient. Hence, find the zeroes of the polynomial x^(3)+2x^(2)+kx-18 .

If ax + by = a^(2)-b^(2) and bx + ay = 0, find the value of x + y .

The number of polynomials of the form x^(3)+ax^(2)+bx+c that are divisible by x^(2)+1 , where a, b,c in{1,2,3,4,5,6,7,8,9,10} , is

When a polynomial 2x ^(3) + 3x ^(2) + ax + b is divided by (x-2) leaves remainder 2, and (x +2) leaves remainder -2. Find a and b.

If the polynomials 2x ^(3) + ax ^(2) + 3x -5 and x ^(3) + x ^(2) - 4x +a leave the same remainder when divided by x -2, find te value of a.