Question

find a quadratic polynomial whose zeroes are alpha and beta are satisfying the relations alpha +beta =3and alpha - beta = - 1.

Answer 1

Hi Mate !!


Here's ur ans :-


Given :-

$\alpha + \beta = 3$


$\alpha - \beta = ( - 1)$


Solution :-

Using identity :-

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

${(3)}^{2} = {( - 1)}^{2} + 4 \alpha \beta$


$9 = 1 + 4 \alpha \beta$


$9 - 1 = 4 \alpha \beta$

$8 = 4 \alpha \beta$

$\frac{8}{4} = \alpha \beta$

$2 = \alpha \beta$


Now , we have Sum of the Zeros as 3 and product of the zeros as 2


♯ To form the quadratic equation we have formula as :-

x² - ( Sum of Zeros )x +(Product of Zeros )

Putting value in the Formula :-

x² - 3x + 2 = 0

Is the required quadratic equation !!

Answer 2

heya
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→ refer to the attachment

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