Question

Find a quadratic polynomial whose zeroes are 4 + √5 and 4 − √5 .​

Answer 1

SOLUTION

TO DETERMINE

The quadratic polynomial whose zeroes are

4 + √5 and 4 − √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 quadratic polynomial has zeroes 4 + √5 and 4 − √5

Sum of the zeroes

= 4 + √5 + 4 − √5

= 8

Product of the Zeroes

= ( 4 + √5) ( 4 − √5 )

$= {4}^{2} - {( \sqrt{5} )}^{2}$

$= 16 - 5$

$= 11$

Hence the required Quadratic polynomial is

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

$= \sf{ {x}^{2} - 8x + 11 }$

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