Question

for what value of k will the sum of the roots of the equation X ^2- x equal to k (5 x - 1) is zero​

Answer 1

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For what value of k are the roots of the quadratic equation x2−(3k−1)x−2k2+2k+11=0 equal. 

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Given,

x2−(3k−1)x−2k2+2k+11=0

condition for roots to be equal is,

b2=4ac

[−(3k−1)]2=4(1)(−2k2+2k+11)

9k2+1−6k=−8k2+8k+44

17k2−14k−43=0

k=2a−b±b2−4ac

=2(17)14±(−14)2−4(17)(−43)

∴k=177±2195