Question

write a quadratic polynomial sum of whose zeroes is 2 and product is -8
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Answer 1

SOLUTION :

TO DETERMINE

The quadratic polynomial the sum and product of whose zeroes are 2 and - 8 respectively

FORMULA TO BE IMPLEMENTED

The quadratic polynomial whose zeroes are given can be written as

$\sf{}{x}^{2} - (Sum \:of \:the \: zeros)x + (Product \:of \:the \: zeros)$

EVALUATION

The required Quadratic polynomial is

$\sf{}{x}^{2} - (Sum \:of \:the \: zeros)x + (Product \:of \:the \: zeros)$

$= \sf{} {x}^{2} - 2x - 8$

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ADDITIONAL INFORMATION

A general equation of quadratic equation is

$a {x}^{2} + bx + c = 0$

Now one of the way to solve this equation is by SRIDHAR ACHARYYA formula

For any quadratic equation

$a {x}^{2} + bx + c = 0$

The roots are given by

$\displaystyle \: x = \frac{ - b \pm \: \sqrt{ {b}^{2} - 4ac } }{2a}$

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where α=5+2√6 and αβ=1 is

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Answer 2

Given the sum of roots 2

product of roots -8

Quadratic equation:- x^2-(sum of roots)x + product of roots

x^2-2x-8 is the final quadratic equation