If the equation


If the equation 2x2 – kx + x + 8 = 0 has real and equal roots, then k = __________.


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 $b=-k+1$



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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