Multiple choice

The equation $kx^2+x+k=0$ and $kx^2+kx+1=0$ have exactly one root in common for

  1. $\displaystyle k=-\frac { 1 }{ 2 } ,1$
  2. `$k=1$
  3. $\displaystyle k=-\frac { 1 }{ 2 } $
  4. $\displaystyle k=\frac { 1 }{ 2 } $
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Subtracting the two equations: (k-k)x^2 + (1-k)x + (k-1) = 0 => (1-k)x = 1-k. If k=1, 0=0 (infinitely many solutions). If k != 1, x=1. Substituting x=1 into kx^2+x+k=0 gives 2k+1=0, so k = -1/2.

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