Multiple choice

One of the roots of the equation ax² − (6a + 5)x + 120 = 0 is 8. Find the other root of the equation.

  1. 11

  2. 9

  3. -3

  4. 7

  5. 5
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

If 8 is a root, then a(8^2) - (6a+5)(8) + 120 = 0. 64a - 48a - 40 + 120 = 0, so 16a = -80, a = -5. The equation is -5x^2 - (-30+5)x + 120 = 0, or -5x^2 + 25x + 120 = 0. Dividing by -5: x^2 - 5x - 24 = 0. Roots are (x-8)(x+3)=0. The other root is -3.

AI explanation

Substituting the known root 8 into the equation gives 64a minus 48a minus 40 plus 120 equals zero, which simplifies to 16a equals negative 80 and yields a equals negative 5. Plugging this value back gives negative 5x squared plus 25x plus 120 equals zero, which simplifies to x squared minus 5x minus 24 equals zero. Factoring this quadratic yields the roots 8 and negative 3, so the other root is negative 3.

Keep practicing — related questions