Question

a quadratic polynomial whose zeroes are 5 and -2 is​

Answer 1

Step-by-step explanation:

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Answer 2

$\displaystyle\huge\red{\underline{\underline{Solution}}}$

FORMULA TO BE IMPLEMENTED

If the zeroes of the quadratic polynomial are given, then the quadratic polynomial is obtained as

${x}^{2} - ( \: sum \: of \: the \: zeros \: )x + product \: of \: the \: zeros \:$

GIVEN

A quadratic polynomial, whose zeroes are 5 and -2

TO DETERMINE

The quadratic polynomial

EVALUATION

The Zeros are 5 & - 2

So

Sum of the zeroes

= 5 + (-2)

= 5-2

= 3

Product of the Zeros

= (5) × (-2)

= - 10

So the required polynomial is

${x}^{2} - ( \: sum \: of \: the \: zeros \: )x + product \: of \: the \: zeros \:$

$= {x}^{2} - ( 3)x-10$

$= {x}^{2} - 3x - 10$