Question
Find all the common zeroes of the polynomials x3+5x2−9x−45 and x3+8x2+15x.
Answer: Option C
:
C and D
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C and D
Let p(x)=x3+5x2−9x−45
q(x)=x3+8x2+15x
p(x)=x3+5x2−9x−45
p(x)=x2(x+5)−9(x+5)
p(x)=(x+5)(x2−9)
p(x)=(x+5)(x+3)(x−3)
⇒ 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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