Question

Given that x-√5is is a factor of the cubic
polynamial
x^3-3√5x^2+13-3√5 find all the zerdes
of the polynomial​

Answer 1

Step-by-step explanation:

Sol : given that x-√5 is a factor of the cubic polynomial x3-3√5x2+13x-3√5 x-√5 ) x3-3√5x2+13x-3√5 ( x2 -2√5x + 3 x3- √5x2 ( subtract )

------------------------------- - 2√5x2+13x - 2√5x2+10x ( subtract ) ------------------------------ 3x - 3√5 3x - 3√5 ( subtract ) ------------------------ 0 ∴ The quotient is x2 -2√5x + 3 = 0 Using roots of quadratic formula a = 1, b = 2√5, c = 3 x = (-b ± √(b2 - 4ac) ) / 2a x = (2√5 ± √((2√5)2 - 12) ) / 2 ∴ the other zeros are x = √5 ± √2