Question

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

Answer 1

$\bold \pink{ \star \: format \star} \\ \red{ {x}^{2} - (sum \: of \: zeroes)x +(product \: of \: zeroes) } \\ {x}^{2} - ( - 4 + 5)x + (4 \times - 5) \\ = > {x}^{2} - ( - 1)x + ( - 20) \\ = > {x}^{2} + x - 20$

Answer 2

SOLUTION

TO DETERMINE

The quadratic polynomial, whose zeroes are - 4 and - 5

CONCEPT TO BE IMPLEMENTED

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

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

EVALUATION

Here it is given that for the given Quadratic polynomial zeroes are - 4 and - 5

Sum of the zeroes = - 4 - 5 = - 9

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

Hence the required Quadratic polynomial

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

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

$\bf{ = {x}^{2} + 9x + 20 }$

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