Question

8 Form a quadratic polynomial whose one of the zeroes is -15 and sum of the
zeroes is 42.

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Answer 1

GIVEN :-

$let \: the \: zeros \: of \: the \: polynomial \: be \: \alpha \: and \: \beta \\ \\ \alpha = - 15 \\ \\ \beta + \alpha = 42$

TO FIND :- The polynomial p(x)

SOLUTION :-

$\alpha + \beta = 42 \\ \\ \\ \implies - 15 + \beta = 42 \\ \\ \\ \implies \beta = 57$

Now, to form a quadratic polynomial we should have the product of the zeros :-

$\alpha \beta \\ \\ = - 15 \times 57 \\ \\ = - 855$

We can use the below formula for finding the Polynomial P(x)

$p(x) = {x}^{2} - ( \alpha + \beta )x + \alpha \beta \\ \\ = {x}^{2} - 42x - 855 \: \: \: (ans)$