Question

A quadratic polynomial, whose zeroes are -4 and -5, is​

Answer 1

Step-by-step explanation:

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Answer 2

The required quadratic polynomial whose zeroes are - 4 , - 5 is x² + 9x + 20

Given :

The zeroes of a quadratic polynomial are - 4 , - 5

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 - 4 , - 5

Sum of zeroes = ( - 4 ) + ( - 5 ) = - 4 - 5 = - 9

Product of the zeroes = - 4 × ( - 5 ) = 20

Step 2 of 2 :

Find the quadratic polynomial

The required quadratic polynomial

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

$\displaystyle \sf = {x}^{2} - (-9)x + 20$

$\displaystyle \sf = {x}^{2} + 9x + 20$

Hence the quadratic polynomial whose zeroes are - 4 , - 5 is x² + 9x + 20

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