Question

obtain all other zeros of the polynomial x^4+2x^3-13x^2- 38x-24 if two of its zeros are -1 and -2​

Answer 1

Hi friend,

Here's ur solution -

Let, p(x)= x⁴+2x³-13x²-38x-24

Since, -1 and -2 are the two zeros of the polynomial.

(x+1)(x+2) = x²+2x+x+2

g(x)= x²+3x+2

On dividing p(x) by g(x).

We get ,

q(x)=x²-x-12

= x²-4x+3x-12

=x(x-4)+3(x-4)

=(x-4)(x+3)

One of the zero is 4 and other zero is -3.

Also , -2 and -1 are the given zeros