Multiple choice

If one root of quadratic equation ${ x }^{ 2 }-x+3m=0$ is 4 times the root of the equation ${ x }^{ 2 }-x+m=,0$ where m$\neq 0,$ then m equals

  1. $\dfrac { 12 }{ 196 } $
  2. $\dfrac { 12 }{ 169 } $
  3. $\dfrac { 12 }{ 256 } $
  4. $\dfrac { 12 }{ 189 } $
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let r be the relevant root of x^2 - x + m = 0. The corresponding root of x^2 - x + 3m = 0 is 4r. Using r^2 - r + m = 0 and 16r^2 - 4r + 3m = 0 gives r = 1/13, so m = r - r^2 = 12/169.

Keep practicing — related questions