Multiple choice

If the equation 2x2 - 6x + m = 0 has two distinct roots a and b, and ab and (a + b) are the distinct roots of the equation y2 + ry + r = 0, then the value of 16(r - m) is ___.

  1. -16

  2. -12

  3. -8

  4. 0

  5. 8
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

For 2x^2 - 6x + m = 0, a+b = 3 and ab = m/2. The roots of y^2 + ry + r = 0 are ab and a+b. Thus, m/2 + 3 = -r and (m/2)*3 = r. Solving these, 3m/2 = -m/2 - 3 gives 2m = -3, m = -1.5, r = -2.25. Then 16(r - m) = 16(-2.25 - (-1.5)) = 16(-0.75) = -12.

Keep practicing — related questions