Question

If two zeroes of polynomial is 2 and -2then find new polynomial

Answer 1

Heya !!

Here's your answer..⬇
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$let \: \: \alpha \: \: and \: \: \beta \: \: are \: \: zeros \: \: \\ of \: \: a \: \: quadratic \: \: polynomial \: \: \\ \\ p(x) = a {x}^{2} + bx + c = 0 \\ \\ (x - \alpha ) \: \: and \: \: (x - \beta ) \: \: are \: \: factor \: \: of \: \: p(x) \\ \\ \alpha = 2 \\ \\ \beta = - 2 \\ \\ sum \: \: of \: \: zer os \: = \alpha + \beta \\ \\ = 2 - 2 \\ \\ = 0 \\ \\ product \: \: of \: \: zeros \: = \alpha \times \beta \\ \\ = 2 \times - 2 \\ \\ = - 4 \\ \\ a {x}^{2} + bx + c = (x - \alpha )(x - \beta ) \\ \\ = {x}^{2} - \alpha x - \beta x + \alpha \beta \\ \\ = {x}^{2} - ( \alpha + \beta )x + \alpha \beta \\ \\ = {x}^{2} - 0 + ( - 4) \\ \\ = {x}^{2} - 0 - 4 \\ \\ = {x}^{2} - 4$
New p(x) = x² - 4
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Hope it helps..
Thanks :)