Question

if the sum of zeroes of polynomial 3x²-kx+1 is equal to its product then value of k is​

Answer 1

$\huge \bold \color{green}{ \underline{ \underline \red{required \: answer :- }}}$

polynomial:- 3x²-kx+1 = 0

given:- sum of zeroes = product of zeroes

solution:-

$\bold{let \: \alpha \: \: is \: sum \: of \: zeroes \:} \\ and \: \\ \bold{ \beta \: is \: the \: product \: of \: zeroes}$

according to question,

$\huge \alpha = \beta$

and we know that..

if the equation is in the form of ax²+bx+c = 0

$so \: sum \: of \: zeroes = \huge\frac{ - b}{a}$

and

$poduct \: of \: zeroes \: = \huge \frac{c}{a}$

in polynomial 3x²-kx+1 = 0

• a = 3
• b = -k
• c = 1

so

$\huge\alpha = \frac{ - ( - k)}{3}$

and

$\huge \beta = \frac{1}{3}$

$\: since \: \: \: \alpha = \beta \\ \\ \: so \: \: \frac{ - ( - k)}{3} = \frac{1}{3} \\ \\ \: \implies \: k = 1$

$\bold{so \: value \: of \: k \: is \: 1}$