Question

if 2x-1 is a factor of 4x^2-kx+k find the value of k

Answer 1

This is the answer for the question.Ignore the blue spread as it was my work.Hope it helps...

Answer 2

✴✴$\huge \bf{HEY \: FRIENDS!!}$✴✴

--------------------------------------------------------

✴✴$\huge \bf \underline{ Here \: is \: your \: answer↓}$⬇⏬⤵


⬇⬇⬇⬇⬇⬇⬇⬇⬇⬇⬇⬇⬇⬇

▶⏩$\sf{It \: is \: given \: that:-)}$

▶⏩$\sf{2x - 1 \: is \: the \: factor \: of \: {4x}^{2} - kx + k.}$

=> 2x - 1 = 0.

$\huge \boxed{x = \frac{1}{2} .}$

$\bf \underline{Using \: factor \: theorem:-)}$

$\bf{=> p(x) = 4 {x}^{2} - kx +k = 0.}$

$\bf{ = > p( \frac{1}{2} ) = x { (\frac{1}{2} )}^{2} - k \frac{1}{2} + k = 0.}$

$\bf{ = > p = 1 - \frac{k}{2} + k = 0.}$

$\bf{ = > p = \frac{2 - k + 2k}{2} = 0.}$

$\bf{= > 2 + k = 0.}$

$\huge \boxed{k = - 2}$

✅✅ Hence, the value of ‘k’ was finded.✔✔

✴✴$\huge \boxed{THANKS}$✴✴

☺☺☺$\huge \bf \underline{Hope \: it \: is \: helpful \: for \: you}$✌✌✌.