Question

find value of a,(x-1) is the factor of a2×x3-4ax+4a-1​

Answer 1

$\sf \Large Solution!!$

Factor Theorem → When a polynomial f(x) is divided by x - a, the remainder = f(a). And, if the reminder (f(a) = 0; x - a is a factor of the polynomial f(x).

x - 1 = 0

x = 1

Given that (x - 1) is a factor of (a² × x³ - 4ax + 4a - 1). So, the remainder will be 0.

f(x) = a² × x² - 4ax + 4a - 1

f(1) = a² × (1)² - 4a(1) + 4a - 1

0 = a² - 4a + 4a - 1

0 = a² - 1

a² = 1

a = (1)²

a = 1