Multiple choice

If the sum of the roots of the equation $ 5x^{2}-4x+2+k (4x^{2}-2x-1)=0 $ is $6$, then $k =$

  1. $-1$
  2. $1$
  3. $\displaystyle \frac{13}{11}$
  4. $\displaystyle \frac {-13}{11}$
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D Correct answer
Explanation

The equation is (5+4k)x^2 - (4+2k)x + (2-k) = 0. Sum of roots = -b/a = (4+2k)/(5+4k) = 6. 4+2k = 30+24k. -22k = 26. k = -26/22 = -13/11.

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