Question

if the sum of the zeroes of the polynomial x2-(k+6)x+2(2k-1) is equal to the product of it's zeroes. find the value of k.​

Answer 1

Given,

• p(x) = x² - (k+6)x + 2(2k+1)

$\bold{Sum \: of \: zeroes = \frac{ - ( - (k + 6))}{1} }$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \bold{ k + 6}$

$\bold{Product \: of \: zeroes = \frac{2(2k + 1)}{1} }$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \bold{ 4k + 2}$

According to the question,

★ k + 6 = 4k + 2

→ 4k - k = 6 - 2

→ 3k = 4

→ $\large\boxed{\bold{k\:=\frac{4}{3}}}$