Question

$if \: \alpha \: and \: \beta are \: the \: roots \: of \: a \: quadratic \: polynomial \: p(x) = {k}^{2} - \: (k - 6)x \: + (2k + 1). \: find \: the \: value \: of \: k \: \: if \: \alpha + \beta = \alpha \beta$

Answer 1

given : if alpha and beta are the roots of p(X)= k²-(k-6)x + (2k+1), find the value of k , if alpha+beta = alpha x beta

____________________________________

TOPIC: QUADRATIC POLYNOMIAL

TO FIND= THE VALUE OF K

SOLUTION:

p(x)= k²-(k-6)x + (2k+1),

here,

a= 1 , b = k-6 and c= 2k+1

we know that,

sum of zeroes= -b/a

$\alpha + \beta = - (k - 6) = 6 - k$
also,

Product of zeroes= c/a

$\alpha \beta = 2k + 1$

it is given that,

$\alpha + \beta = \alpha \beta$
so,

$6 - k = 2k + 1 \\ \\ 6 - 1 = 2k + k \\ \\5 = 3k \\ \\ k = \frac{5}{3}$