`P(x)=x^3 + ax^2 - x+ b` and
Find a and b so that both x-1 and x-2 are factors of P(x).

If f(x)={{:(1" if "x le 3),(ax+b" if "3 lt x lt 5),(7" if "x ge 5):} Find a and b, so that f(x) is a continuous function.

Find the value of k if x-1 is the factor of P(x)=2x^(2)+kx+sqrt(2)

Find the value of a if (x - 5) is a factor of (x^(3)-3x^(2)+ax-10)

If both (x-2) and (x-(1)/(2)) are factors of (ax^(2)+5x+b) show that a=b

Find the value of k if x-1 is the factor of P(x) =kx^(2)-sqrt(2)x+1

Find the values of a and b for which zeros of q(x) = x^(3) + 2x^(2) +a are also the zero of p(x) = x^(5) - x^(4) - 4x^(3) + 3x^(2) + 3x +bp . Also, find zeros of p(x) which are not zeros of q(x) .

Let for a != a_1 != 0 , f(x)=ax^2+bx+c , g(x)=a_1x^2+b_1x+c_1 and p(x) = f(x) - g(x) . If p(x) = 0 only for x = -1 and p(-2) = 2 then the value of p(2) .

If f(x) = x^(3) + x^(2) - ax + b is divisible by x^(2) - x , find values of a and b .