Question

If a and ß are the zeroes of the
polynomial :
(1 Point)
x² + 4x
+ 3, then the value of a2 B + ab2 will

Answer 1

Correct Question -

If $\alpha$ and $\beta$ are zeros of polynomial x² + 4x + 3 , then find the value of ${ \alpha }^{2} \beta + { \beta }^{2} \alpha$

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Answer

Given -

Quadratic Polynomial - x² + 4x + 3 whose zeros are $\alpha$ and $\beta$

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To find -

${ \alpha }^{2} \beta + { \beta }^{2} \alpha$

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Formula used -

Sum of roots = $\alpha + \beta = -b/a$

Product of roots = $\alpha \beta = c/a$

where

$\longrightarrow$a is coefficient of x²

$\longrightarrow$b is coefficient of x

$\longrightarrow$c is constant

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Solution

$\longrightarrow$a = 1

$\longrightarrow$b = 4

$\longrightarrow$c = 3

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$\longrightarrow$$\alpha + \beta = -4$

$\longrightarrow$$\alpha \beta = 3$

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${ \alpha }^{2} \beta + { \beta }^{2} \alpha = \alpha \beta ( \alpha + \beta )$

Substituting the value of $\alpha + \beta$ and $\alpha \beta$

${ \alpha }^{2} \beta + { \beta }^{2} \alpha = 3 ( - 4 )$

= - 12

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Thanks