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Question

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

A
3 and 5
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B
3 and 5
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C
3 and 5
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D
3 and 5
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Solution

The correct option is D 3 and 5

Let:

P(x)=x3+5x29x45 ; Q(x)=x3+8x2+15x

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

P(x)=(x+5)(x29)

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

Zeroes of x3+5x29x45 are -5,-3 and 3.

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

Q(x)=x(x+5)(x+3)

Zeroes of x3+8x2+15x are 0,-5 and -3.

common zeroes are -5 and -3.


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