Question

The value of k for which equ equation,
2x²-kx+k=0 has equal root is
a)-4 b)4 c)8 d)-8​

Answer 1

$\;\;\underline{\textbf{\textsf{ Given:-}}}$

• A quadratic equation is____

2x² - kx + k = 0

Where,

• The roots of the given equation are equal.

$\;\;\underline{\textbf{\textsf{ To Find :-}}}$

• The value of k

$\;\;\underline{\textbf{\textsf{ Solution :-}}}$

Given that,

Quadratic equation

2x² - kx + k = 0

Where the roots of the equation are equal. Then it's discriminate (D) will be 0.

Here,

a = 2

b = -k

c = k

$\underline{\:\textsf{ Putting the given values :}}$

$\sf \longrightarrow {b}^{2} - 4ac = 0 \\ \\ \sf\longrightarrow ( - k) {}^{2} - 4 \times 2 \times k = 0 \\ \\ \sf \longrightarrow {k}^{2} - 8k = 0 \\ \\ \sf \longrightarrow k(k - 8) = 0$

$\sf \longrightarrow k = 0 \: \:or\:\longrightarrow k = 8$

$\;\;\underline{\textbf{\textsf{ Hence-}}}$

$\underline{\textsf{ The value k is \textbf{8 }}}.$

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$\boldsymbol{\: Option\:C)\: is \: correct√}$

Answer 2

Step-by-step explanation:

option c is correct ✅