Question

plz I m not understanding help me how this came (alpha-beta)^2 and that -4aplha× beta
this first line​

Answer 1

First, I'll solve the question for you.

Given polynomial:

$f(x) = x^2 + px + 45$

Sum of Zeroes $= \alpha + \beta = -p$

Product of Zeroes $= \alpha \beta = 45$

Now, According to the question,

$(\alpha - \beta)^2 = 144\\\\\implies \alpha ^2 + \beta ^2 - 2 \alpha \beta = 144\\\\\implies (\alpha + \beta)^2 - 2 \alpha \beta - 2 \alpha \beta = 144\\\\\implies (\alpha + \beta)^2 - 4 \alpha \beta = 144\\\\\implies (-p)^2 - 4(45) = 144\\\\\implies p^2 - 180 = 144\\\\\implies p^2 = 144 + 180 = 324\\\\\implies p = \pm \sqrt{324} = \boxed{\pm 18}$

±18 is the answer to the question.

Answer 2

《 Thanks for your question》

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