Question

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

Answer 1

Answer: x^2 - x + 1

Step-by-step explanation:

Sum of zeroes - 0 + 1 = 1

Product of zeroes 0 x 1 = 1

New polynomial =k (x^2 -(Sum)x + Product)

=k (x^2 -1x + 1)

= x^2 - x + 1

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 the zeroes of the quadratic polynomial are - 4 and - 5

Sum of the zeroes

= ( - 4 ) + ( - 5 )

= - 4 - 5

= - 9

Product of the zeroes

= ( - 4 ) × ( - 5 )

= 20

Hence the required Quadratic polynomial is

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

= x² + 9x + 20

FINAL ANSWER

Hence the required Quadratic polynomial is

x² + 9x + 20

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