Question

Number of quadratic polynomial having 4 and 7 as their two zeroes ​

Answer 1

SOLUTION

TO DETERMINE

Number of quadratic polynomial having 4 and 7 as their two zeroes

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

We have to find the number of quadratic polynomial having 4 and 7 as their two zeroes

Sum of the zeroes = 4 + 7 = 11

Product of the zeroes = 4 × 7 = 28

So the required Quadratic polynomial

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

$= \sf{ {x}^{2} - 11x + 28 }$

Hence the number of quadratic polynomial having 4 and 7 as their two zeroes = 1

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