Please help me solve rational zero problem

**runner940** · February 27th 2009, 04:25 PM

Can someone help me find the zeros to this equation? I have tried all possible zeros and none of them work!

Equation is : d^3+5d^2+35d+175

**Prove It** · February 27th 2009, 04:36 PM

Originally Posted by runner940

Can someone help me find the zeros to this equation? I have tried all possible zeros and none of them work!

Equation is : d^3+5d^2+35d+175

$P(d) = d^3 + 5d^2 + 35d + 175 = 0$

Use factorisation by grouping 2 and 2.

$0 = d^3 + 35d + 5d^2 + 175$

$0 = d(d^2 + 35) + 5(d^2 + 35)$

$0 = (d^2 + 35)(d + 5)$ .

Now we can use the null factor law to find the zeros.

$d + 5 = 0$ or $d^2 + 35 = 0$

The only REAL zero is $d = -5$ , and there are 2 complex zeros, namely $d = \pm \sqrt{35}$ .

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