Question

if one of the zero of cubic polynomial x cube + a x square + bx C is -1 then the product of other two zeros is
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Answer 1

In the above Question , the following information is given -

One of the zeroes of the cubic polynomial x³ + ax² + bx + c is -1 .

To find -

Find the product of the other two zeroes .

Solution -

Given Quadratic Polynomial -

=> x³ + ax² + bx + c .

Let the three roots of the equation be α , β and γ respectively.

Now , by vieta relations , we can state that -

Sum of roots -

α + β + γ = - a ............ { 1 }

Sum of roots { Two at a time } -

α β + β γ + α γ = b . ........... { 2 }

Product Of Roots -

α β γ = - c . ............ { 3 }

Now , one of the zeroes , suppose α is -1 .

Now , we can substitute this value in the third equation .

This is -

α β γ = - c

=> { -1 } β γ = - c .

=> β γ = C .

Thus , the product of the other two roots is C .

This is the required answer .

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