Question

Values of k for which the quadratic equation 2x^2 -kx + k = 0 has equal roots is

Answer 1

Answer:

Step-by-step explanation:

Put D=0

b square - 4ac=0

K square -8k=0

K=0,8

Answer 2

$\sf{\underline{\boxed{\green{\large{\bold{ Solution}}}}}}$

$\sf\implies 2x^2 - kx + k = 0$

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• compare the eq with $\sf{\underline{\bold{ax^2 + bx + c = 0 }}}$

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☯ a = 2

☯ b = -k

☯ c = k

• Given that the equation has real roots .
• Therefore $\sf{\underline{\bold{ D = 0 }}}$

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$\sf{\underline{\boxed{\pink{\large{\mathfrak{ D = b^2 - 4ac }}}}}}$

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$\sf\implies 0 = (-k)^2 - 4 \times 2 \times -k$

$\sf\implies 0 = k^2 + 8k$

$\sf\implies k( k + 8 ) = 0$

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$\begin{tabular}{|c|c|}\cline{1-2}\sf k = 0 &\sf k + 8 = 0 \\\cline{1-2}\sf k = 0 &\sf k = -8 \\\cline{1-2}\end{tabular}$

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$\sf{\underline{\boxed{\purple{\large{\bold{ k = 0 \: or \:-8 }}}}}}$

• Therefore the complete equation is $\sf{\bold{\underline{2x^2 + 8x - 8 = 0 }}}$