Question

Optain all other zeroes of the polynomial x^4+7x^3+7x2 -35x-60 if two of its zeros are -3 and -4

Answer 1

Concept Introduction:

Zero of equation means if the value is put into equation the result that will come is zero.

Given: Two of its zeros of the given polynomial are $-3$ and $-4$.

To Find:

We have to find the value of, other two zeros.

Solution:

According to the problem,

$-3$ and $-4$ are zeros of the polynomial.

$(x+3)(x+4)=x^{2} +7x+12$

Now, $\frac{x^4+7x^3+7x2 -35x-60}{x^{2} +7x+12} =x^{2} -5$

⇒ $x^{2} -5=0$

⇒$x=+\sqrt{5}$ or $x=-\sqrt{5}$

Final Answer:

The value of other two zeros are $x=+\sqrt{5}$ or $x=-\sqrt{5}$.

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