Question

If x=2 & x=0 are the roots of the polynomial p(x) = 2x^3-5x^2+ax+b, find a & b

Answer 1

Answer:

The value of a=2 The value of y=0

Answer 2

ANSWER :–

a = 2 & b = 0

EXPLANATION :–

GIVEN :–

A polynomial function P(x) = 2x³ - 5x² + ax + b have two roots x = 2 and x = 0 .

TO FIND :–

Values of a and b .

SOLUTION :–

☞ Roots of a polynomial will satisfy the equation.

So that –

• At x = 0 –

➨ p(0) = 0

➨ 2 (0)³ - 5 (0)² + a(0) + b = 0

➨ b = 0 ———————(1)

• Now at x = 2 –

➨ p(2) = 0

➨ 2(2)³ - 5 (2)² + a(2) + b = 0

➨ 16 - 20 + 2a + 0 = 0 [ using eq.(1) ]

➨ -4 + 2a = 0

➨ 2a = 4

➨ a = 2