Question

the quadratic polynomial having zeros - 2 and 4 is​

Answer 1

REFER TO THE ATTACHMENT:

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Answer 2

The quadratic polynomial having zeros - 2 and 4 is x² - 2x - 8

Given :

The zeroes of a quadratic polynomial are - 2 and 4

To find :

The quadratic polynomial

Concept :

If the Sum of zeroes and Product of the zeroes of a quadratic polynomial is given then the quadratic polynomial is

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

Solution :

Step 1 of 2 :

Find Sum of zeroes and Product of the zeroes

Here it is given that zeroes of a quadratic polynomial are - 2 and 4

Sum of zeroes = - 2 + 4 = 2

Product of the zeroes = ( - 2) × 4 = - 8

Step 2 of 2 :

Find the quadratic polynomial

The required quadratic polynomial

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

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

Hence the quadratic polynomial having zeros - 2 and 4 is x² - 2x - 8

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