Question

The quadratic equation 2x²+2Kx+√2K=0 has equal roots if K=
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Answer 1

$\color{red}{\huge{\underline{GIVEN\dag}}}$

• $2 {x}^{2} + 2kx + \sqrt{2} k = 0$
• Has equal roots

$\color{red}{\huge{\underline{SOLUTION\dag}}}$

We know that,

when roots are equal discriminant is equal to zero.

$⇒ {b}^{2} - 4ac = 0$

Here,

• $a=2$
• $b=2k$
• $c=\sqrt{2}k$

$⇒ ({2k})^{2} - 4(2)( \sqrt{2} k) = 0$

$⇒4 {k}^{2} - 8 \sqrt{2} k = 0$

$⇒4k(2k - \sqrt{2} ) = 0$

$⇒2k - \sqrt{2} = 0$

$2k = \sqrt{2}$

$\color{indigo}{{\boxed{k = \frac{ \sqrt{2} }{2}}}}$

HOPE THAT HELPS!!