Question

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

Answer 1

let p(x)=x^4+2x^3-13x^2-38x-24

-1 and -2 are two zeroes of p(x)

p(x)=(x+1)(x+2)(x^2-x-12)

=(x+1)(x+2)[x^2-4x+3x-12]

=(x+1)(x+2)[x(x-4)+3(x-4)]

=(x+1)(x+2)(x-4)(x+3)

therefore other two factors are
(x-4)(x+3)

two zeroes are 4 and -3

Answer 2

Answer:

4 and -3

Step-by-step explanation:

let p(x)=x^4+2x^3-13x^2-38x-24

• -1 and -2 are two zeroes of p(x)

• p(x)=(x+1)(x+2)(x^2-x-12)

• =(x+1)(x+2)[x^2-4x+3x-12]

• =(x+1)(x+2)[x(x-4)+3(x-4)]

• =(x+1)(x+2)(x-4)(x+3)

therefore other two factors are

• (x-4)(x+3)

• two zeroes are 4 and -3