Given that `x^(2)+x-6` is a factor of `2x^(4)+x^(3)-ax^(2)+bx+a +b-1`, find the values of a and b.

p(x)= ax^2+bx+5 :- If (x^2-1) is a factor of p(x),then find the value of a and b?

If (x-1) is to be a factor of p(x) = a^2x^2-4ax + 4a-1 .What should be the value of ‘a’ ?

The curve f(x) = (x^(2) + ax + b)/(x - 10) has a stationary point at (4, 1). Find the values of a and b. Also, show that f(x) has point of maxima at this point.

If (x+1) and (x -1) are factors of x^3+2x^2 + px + q , find p and q.

If the curve y = ax^(2) - 6x + b passes through (0, 2) and has its tangent parallel to the x-axis at x = (3)/(2) , then find the values of a and b.

Given x-1 is a factor of x^2+ax+b .Prove that (a+b= -1) .

Given 'x-1' is a factor of x^2+a x+b Prove that 'a+b=-1'

The function y = (ax + b)/((x - 1)(x - 4)) has turning point at P(2, -1). Then find the values of a and b.