The values of ’k’ for which the equation 2x^2 – kx + x + 8 = 0 will have real and equal roots are ……………
The values of ’k’ for which the equation 2x2 – kx + x + 8 = 0 will have real and equal roots are ……………
A) 9 and -7
B)-9 and 7
C) only 9
D) only -7
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Correct option is (A) 9 and -7
Given equation is
\(2x^2-kx+x+8=0\)
\(\Rightarrow\) \(2x^2+(1-k)x+8=0\)
For equal roots, we have
Discriminant = 0
\(\Rightarrow(1-k^2)-4\times2\times8=0\)
\(\Rightarrow(1-k^2)=64\)
\(\Rightarrow1-k=\pm8\)
\(\Rightarrow1-k=8\) \(or\;1-k=-8\)
\(\Rightarrow k=1-8=-7\) \(or\;k=1+8=9\)
Hence, the possible values of k are -7 & 9 for equal roots.
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