Question

Obtain other zeroes of the polynomial
p(x) = 2x4 – x3 – 11x2 + 5x + 5
if two of its zeroes are and-
$- \sqrt{5}$

$\sqrt{5}$

O​

Answer 1

Answer:1, -1/2

$x=\pm\sqrt{5}$

Square both sides

$x^2-5=0$

Why I did this is because

two of its zeroes come from equation above

Now divide p(x) by x²-5

Division ends without remainder. Quotient : 2x²-x-1

Factor 2x²-x-1

→ (2x+1)x-(2x+1)

→ (2x+1)(x-1)

By the factoring method

Two zeros are $1$ and $-\frac{1}{2}$.