Condition for Polynomial with repeated roots

Condition of Common Roots

Condition of Common Roots

Let f(x) be a cubic polynomial such that x=1 is a repeated root of order 2 and x=(5)/(3) is a point of local Minima.If int_(0)^(1)f(x)dx=(-7)/(12) then

Statement-1: There is a value of k for which the equation x^(3) - 3x + k = 0 has a root between 0 and 1. Statement-2: Between any two real roots of a polynomial there is a root of its derivation.

Find a polynomial with sum of roots as 7 and product of roots as 3.

A quadratic polynomial with two distinct roots has one real root. Then, the other root is

Statement-1: If f(x) = 1 + x + (x^(2))/(2!) + (x^(3))/(3!) + (x^(4))/(4!) , then the equation f(x) = 0 has two pairs of repeated roots. Statement-2 Polynomial equation P(x) = 0 has repeated root alpha , if P(alpha) = 0 and P'(alpha) = f0

Draw the Graph of the Polynomial when roots of the polynomial is given.

Finding square root through repeated subtraction