Multiple choice

Which of the following is one of the roots of the quadratic equation 12(1 - y2) = 7y?

  1. 4/3

  2. -4/3

  3. -3/4

  4. -3

  5. 4
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Rearranging gives 12y^2 + 7y - 12 = 0. Factoring or applying the quadratic formula gives roots 3/4 and -4/3, so -4/3 is one of the roots.

AI explanation

We first write the given equation 12(1 - y^2) = 7y in standard quadratic form by moving all terms to one side, resulting in 12y^2 + 7y - 12 = 0. We then factor this quadratic equation by finding two numbers that multiply to -144 and add to 7, which are 16 and -9. This allows us to write the middle term as 16y - 9y, so the factored form is (3y + 4)(4y - 3) = 0. Setting each factor to zero gives y = -4/3 or y = 3/4.

Keep practicing — related questions