Question

obtain all zeros of the polynomial 2x^4-10x^3+5x^2+15x-12 if two of its zeros are root 3/root 2 and -root3/root2

please don't simply watch please do the answer by explanation ​

Answer 1

p(x)=2x^4-10x3+5x2+15x-12

x= -√3/2 and √13/2

Therefore,(x+√3/2)(x-√3/2)=0

x²-3/2=0

(2x2-3)/2=0

2x2-3=0

g(x)=2x2-3

Now divide p(x) by g(x)

The q(x) will be

=x²-5x+4

=x2-4x-x+4

=x(x-4)-1(x-4)

=(x-4)(x-1)

x=4 and x=1

Therefore, the other two zeroes are 4 and 1.

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