The quadratic polynomial `p(x)` has the following properties:`p(x)geq0` for all real numbers, `p(1)=0a n dp(2)=2` . Find the value of `p(3)` is__________.

The quadratic polynomial p(x) ha following properties p(x) can be positive or zero for all real numbers p(1)=0 and p(2)=2. Then find the quadratic polynomial.

The number of polynomials p:R to R satisfying p(0)=0,p(x) gtx^(2) for all x ne0 , and p''(0)=(1)/(2) is

A quadratic polynomial p(x) is given as p(x)=x^(2)-5x+6, then find the maximum value of (p(cos x))/(2)

For a polynomial p(x) of degree ge1, p(a)=0 , where a is a real number, then (x-a) is a factor of the polynomial p(x) Find the value of k if x-1 is a factor of 4x^(3)+3x^(2)-4x+k .

Find all polynomials p satisfying p(x+1)=p(x)+2x+1

A polynomial P(x) with real coefficients has the property that P^(n)(x)ne0 for all x. Suppose P(0)=1 and P'(0) = -1 . What can you say about P(1)?

Let P(x) be a quadratic polynomial with real coefficients such that for all real x the relation 2(1+P(x))=P(x-1)+P(x+1) holds. If P(0)=8 and P(2)=32, then Sum of all the coefficients of P(x) is:

If the quadratic polynomial p(x) is divisible by x - 4 and 2 is a zero of p(x) then find the polynomial p(x).

Let p(x) be a polynomial of degree 4 having extremum at x=1,2 and lim_(x rarr0)(1+(p(x))/(x^(2)))=2. Then find the value of p(2)

If the roots of the quadratic equation 3x^(2)+5x+3(4p-1)=0 is reciprocal of each other. Find the value of p