Multiple choice

One root of the equation 5x2 + 2x + Q = 2 is reciprocal of another. What is the value of Q2?

  1. 25

  2. 1

  3. 49

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

The equation is 5x^2 + 2x + (Q-2) = 0. If one root is the reciprocal of the other, their product is 1. Product of roots = c/a = (Q-2)/5 = 1, so Q-2 = 5, Q = 7. Then Q^2 = 49.

AI explanation

If one root is the reciprocal of the other in the quadratic equation 5x squared plus 2x plus Q minus 2 equals 0, the product of the roots must equal 1. By Vieta's formulas, the product of the roots equals the constant term divided by the leading coefficient, so (Q minus 2) divided by 5 equals 1. Solving this gives Q minus 2 equals 5, making Q equal to 7. The value of Q squared is then 7 squared, which is 49.

Keep practicing — related questions