a) If `p^x div p^4 =1` find the value of `x`

If p = log 20 and q = log 25, find the value of x, if 2 log(x + 1) = 2p - q.

Let If the set of values of k for which f(x) 0 is (p,q) then find the value of (4p+3q), where f(x)=kx^2+x(3-4k)-12.

If 1 is a zero of the polynomial p(x) = ax^2 — 3 (a — 1) x - 1 , then find the value of a.

if p = (4xy)/(x + y) , find the value of (p+2x)/(p-2x) + (p+2y)/(p-2y) .

If x+1,\ 3x and 4x+2 are in A.P., find the value of x .

Let a and p be the roots of equation x^2 + x - 3 = 0 . Find the value of the expression 4p^2 - a^3 .

Let f(x)= x^(3) + x + 1 and P(x) be a cubic polynomial such that P(0) = -1 and roots of f(0) = 1 ; P(x) = 0 are the squares of the roots of f(x) = 0 . Then find the value of P(4).

The polynomial px^(3)+4x^(2)-3x+q completely divisible by x^2-1: find the values of p and q. Also for these values of p and q factorize the given polynomial completely.

If (1+x+x^2++x^p)^n=a_0+a_1x+a_2x^2++a_(n p)x^(n p), then find the value of a_1+2a_2+3a_3+ddot+n pa_(n p)dot

The random variable X can take only the values 0, 1, 2. Given that P(X=0) = P(X= 1) = p and E(X^2) = E(X) , then find the value of p