Question

alpha ,beta are the roots of the quadratic polynomial p(x)=x^2-(k-6)x+(2k+1). find the value of k, if alpha+beta=alphabeta

Answer 1

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Answer 2

Given :-

x² - ( k - 6 )x + ( 2k + 1 )

alpha + beta = alpha . beta


Sum of roots =

$\frac{coefficient \: of \: x}{coefficient \: of \: {x}^{2} }$
$\alpha + \beta = \frac{k - 6}{1}$


$\alpha + \beta = k - 6$



Product of Roots :-
$\frac{constant \: term}{coefficient \:of \: {x}^{2} }$


$\alpha \beta = \frac{2k + 1}{1}$


$\alpha \beta = 2k + 1$

$\alpha + \beta = \alpha \beta (given)$

k - 6 = 2k + 1

k - 2k = 1 + 6

- k = 7

k = - 7