Question

If zeroes of a cubic polynomial are 2,3and 5.find the cubic polynomial

Answer 1

Given ,

The zeroes of cubic polynomial are 2 , 3 and 5

We know that ,

If $\tt \alpha$, $\tt \beta$ and$\tt \gamma$ are the zeroes of cubic polynomial , then the cubic polynomial will be

$\tt{ \boxed{ {(x)}^{3} - ( \alpha + \beta + \gamma ) {(x)}^{2} + ( \alpha \beta + \beta \gamma + \alpha \gamma )(x)- ( \alpha \beta \gamma )}}$

Thus ,

$\tt \implies {(x)}^{3} - 10 {(x)}^{2} + (6 + 15 + 10)x - 30$

$\tt \implies {(x)}^{3} - 10 {(x)}^{2} + 31x - 30$

Therefore , the required cubic polynomial is (x)³ - 10(x)² + 31x - 30

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Answer 2

Given ,

The zeroes of cubic polynomial are 2 , 3 and 5

We know that ,

If

$\tt \alpha , \tt \beta and\tt \gamma$

are the zeroes of cubic polynomial , then the cubic polynomial will be

$\tt{ \boxed{ {(x)}^{3} - ( \alpha + \beta + \gamma ) {(x)}^{2} + ( \alpha \beta + \beta \gamma + \alpha \gamma )(x)- ( \alpha \beta \gamma )}}$

Thus ,

$\tt \implies {(x)}^{3} - 10 {(x)}^{2} + (6 + 15 + 10)x - 30 \\ </p><p> \\ </p><p>\tt \implies {(x)}^{3} - 10 {(x)}^{2} + 31x - 30$

Therefore , the required cubic polynomial is (x)³ - 10(x)² + 31x - 30

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