Question

if teh sum of zeores and the product of zeores of the polynomial p(x)=x^2+(k-7) x+(k+1)are equal than k= _______​

Answer 1

Given:

• The sum of zeroes and the product of zeroes of the polynomial p(x)=x²+(k-7) x+(k+1) are equal.

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To find:

• Value of k?

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Solution:

In the given polynomial,

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⌬ p(x)=x²+(k-7) x+(k+1)

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• a = 1
• b = (k - 7)
• c = (k + 1)

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According to the given Question:

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★ Sum of zeroes = Product of zeroes

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$:\implies\sf \dfrac{Cofficient\; of\;x}{Cofficient\;of\;x^2} = \dfrac{Constant\;term}{Cofficient\;of\;x^2}$

$:\implies\sf \dfrac{- b}{c} = \dfrac{c}{a}$

$:\implies\sf \dfrac{- (k - 7)}{1} = \dfrac{(k + 1)}{1}$

$:\implies\sf - (k - 7) = (k + 1)$

$:\implies\sf - k + 7 = k + 1$

$:\implies\sf 7 - 1 = k + k$

$:\implies\sf 6 = 2k$

$:\implies\sf k = \dfrac{6}{2}$

$:\implies{\underline{\boxed{\textsf{\textbf{k = 3}}}}}\;\bigstar$

$\therefore\;\underline{\sf{Value\:of\;k\;is\;3}}$