Question

if -2 is a zero of f (x) =x3+13+32x+20.find all the other zeroes of p(x) it's urgent please give a correct answer​

Answer 1

Given info : -2 is a zero of f(x) = x³ + 13x² + 32x + 20.

To find : all the other zeroes of f(x) are ...

solution : if -2 is a zero of f(x) = x³ + 13x² + 32x + 20.

∴ (x + 2) is a factor of f(x) = x³ + 13x² + 32x + 20.

so divide x³ + 13x² + 32x + 20 by (x + 2) we get quotient and after solving quotient we'll get the other zeroes.

so let's start !

x + 2) x³ + 13x² + 32x + 20(x² + 11x + 10

x³ + 2x²

------------------

11x² + 32x

11x² + 22x

--------------------------

10x + 20

10x + 20

------------------------

0

now, quotient = x² + 11x + 10 , this is a quadratic equation. so just solve it.

x² + x + 10x + 10 = 0

⇒x(x + 1) + 10(x + 10) = 0

⇒(x + 1)(x + 10) = 0

⇒x = -1 and -10

Therefore the other zeroes are -1 and -10.