Question

If 1 and -3 are the zeroes of the polynomial xcube - axsquare - 13x + b find the values of a and b​

Answer 1

Explanation:

f(x) = x³ - ax² - 13x + b.

f(1) = 1³ - a(1)² - 13(1) + b = 0

=> 1 - a - 13 + b = 0, b - a - 12 = 0.

f(-3) = (-3)³ - a(-3)² - 13(-3) + b = 0

=> - 27 - 9a + 39 + b = 0, 12 - 9a + b = 0.

Therefore, b - a - 12 = 12 - 9a + b. 8a = 24, a = 3.

=> b - (3) - 12 = 0, b = 15.