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Question

Find all the common zeroes of the polynomials x3+5x29x45 and x3+8x2+15x.


A

3

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B

5

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C

-3

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D

-5

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Solution

The correct options are
C

-3


D

-5


Let p(x)=x3+5x29x45
q(x)=x3+8x2+15x

p(x)=x3+5x29x45

p(x)=x2(x+5)9(x+5)

p(x)=(x+5)(x29)

p(x)=(x+5)(x+3)(x3)

Zeroes are -5,-3 and 3.

q(x)=x3+8x2+15x

q(x)=x(x2+8x+15)

q(x)=x(x+5)(x+3)

Zeroes are 0, -5 and -3

Therefore, common zeroes are -5 and -3.


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