In the polynomial `p(x)=x^2+a x+b`, `p(3+sqrt2)=0, p(3-sqrt2)=0`. Write this polynomial after finding a and b.

In the polynomial p(x)= a x^ 3 + b x^ 2 + c x + d if p(2)=p(-2), prove that 4a+c=0.

Consider the polynomial P(x)=ax^3-x^2-bx-1 .Find P(1) .

In the polynomial p(x)= 2 x^ 3 − 3 x^ 2 − 11 x − 6 find p(3),p(-2) and p( 2 ). What is its peculiarity?

Write a second degree polynomial 'p(x)' in which p(sqrt2+1)=p(sqrt2-1)=0

In the polynomial p(x)= 2 x^ 3 − 3 x^ 2 − 7 x + 3 , find p(-1),p(-2),p(0),p(2). Of these which is the largest?

Consider the polynomial p(x)= x^2-5x+6 :- Is (2x-1)a factor of p(x)? Why?

In the polynomial x^2+a x+b , what numbers must be taken as a and 'b', to get a polynomial for which '(x-2)' and '(x-3)' as factors?

Write the polynomial p(x)=x^2+4 x+1 as the product of two first degree polynomials. Find the solution of the equation 'p(x)=0'

Write the solution of polynomials p(x) = x^2-7x+12 .

Write the polynomial p(x)=x^2+7 x+12 as the product of first degree polynomials.