Question

Find all the common zeroes of the polynomials $x^3+5x^2-9x-45$ and $x^3+8x^2+15x$.

• A. $3\text{and}5$
• B. $3\text{and}-5$
• C. $-3\text{and}5$
• D. $-3\text{and}-5$

Answer 1

The correct option is D $-3\text{and}-5$

Let:

$P\left(x\right)=x^3+5x^2-9x-45$ ; $Q\left(x\right)=x^3+8x^2+15x$

$P\left(x\right)=x^2(x+5)-9(x+5)$

$P\left(x\right)=(x+5)(x^2-9)$

$P\left(x\right)=(x+5)(x+3)(x-3)$

$\Rightarrow$ Zeroes of $x^3+5x^2-9x-45$ are -5,-3 and 3.

$Q\left(x\right)=x(x^2+8x+15)$

$Q\left(x\right)=x(x+5)(x+3)$

$\Rightarrow$ Zeroes of $x^3+8x^2+15x$ are 0,-5 and -3.

$\therefore$ common zeroes are -5 and -3.