Question

Write the polynomial, the product and sum of whose zeroes are 4 and 6 respectively.​

Answer 1

Answer: x²-4x+6 is the polynomial

Answer 2

SOLUTION

TO DETERMINE

The polynomial, the product and sum of whose zeroes are 4 and 6 respectively

CONCEPT TO BE IMPLEMENTED

If the roots of a quadratic polynomial are 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 polynomial the product and sum of whose zeroes are 4 and 6 respectively

Thus

Sum of the zeroes = 6

Product of the Zeros = 4

Hence the required polynomial

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

$\sf{ = {x}^{2} -6x + 4 }$

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