Question:
If the equation 2x2 – kx + x + 8 = 0 has real and equal roots, then k = __________.
Solution:
for $2 x^{2}-k x+x+8=0$
given; roots one real and equal
i.e. $D=0$ (Discriminat)
i. e. $b^{2}-4 a c=0$
Here $b=-k+1$
$a=2$
$c=8$
with reference to standard equations
$a x^{2}+b x+c=0$
$\Rightarrow(1-K)^{2}-4(2) 8=0$
i.e. $K^{2}+1-2 K-64=0$
i.e. $K^{2}-2 K-63=0$
i. e. $K^{2}-9 K+7 K-63=0$
i.e. $(K-9)(k+7)=0$
i.e. $K=9$ or $-7$
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