Multiple choice

Three equations are given below. Solve the equations and answer the question. I. x2 − 7x + 10 = 0 II. y2 − 5y − 6 = 0 III. z2 − 4z − 12 = 0 P. x z R. x < z < y Which of the following is possible?

  1. Only P follows.

  2. Only Q follows.

  3. Only R follows.

  4. Only P and R follow.

  5. None follows.
Reveal answer Fill a bubble to check yourself
A Correct answer
AI explanation

Factoring equation one, x2 minus 7x plus 10 equals zero, gives (x minus 5)(x minus 2) equals zero, meaning x is 5 or 2. Factoring equation two, y2 minus 5y minus 6 equals zero, gives (y minus 6)(y plus 1) equals zero, meaning y is 6 or minus 1. Factoring equation three, z2 minus 4z minus 12 equals zero, gives (z minus 6)(z plus 2) equals zero, meaning z is 6 or minus 2. Testing these values shows x is always greater than z when comparing the smallest x to the largest z, making statement P true, while z is not always less than y and x is not always greater than y, making only P follow.

Keep practicing — related questions