Multiple choice

If one of the roots of the quadratic equation $a{ x }^{ 2 }-bx+a=0$ is $6$, then the value of $\cfrac { b }{ a } $ is equal to

  1. $\cfrac { 1 }{ 6 } $
  2. $\cfrac { 11 }{ 6 } $
  3. $\cfrac { 37 }{ 6 } $
  4. $\cfrac { 6 }{ 11 } $
  5. $\cfrac { 6 }{ 37 } $
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C Correct answer
Explanation

If 6 is a root of ax^2 - bx + a = 0, then a(6)^2 - b(6) + a = 0. This simplifies to 36a - 6b + a = 0, or 37a = 6b. Dividing by 6a gives b/a = 37/6.

AI explanation

Substitute the root x = 6 into the equation a x squared - b x + a = 0 to get 36a - 6b + a = 0, which simplifies to 37a = 6b. Dividing both sides by a and then by 6 yields b divided by a equals 37 divided by 6. The result is 37/6.

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