Multiple choice

If 3 is a real root of the equation x2 + bx − 15 = 0 and equation x2 + bx + q = 0 has equal roots, then what is the value of q?

  1. 1

  2. -1

  3. 2

  4. -2

  5. None of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

If 3 is a root of x^2 + bx - 15 = 0, then 9 + 3b - 15 = 0, so 3b = 6, b = 2. The second equation is x^2 + 2x + q = 0. For equal roots, the discriminant D = b^2 - 4ac = 0. So 2^2 - 4(1)(q) = 0, which means 4 - 4q = 0, so q = 1.

AI explanation

Substitute the real root x = 3 into the first equation, x^2 + bx - 15 = 0, to get 9 + 3b - 15 = 0. Solving this gives 3b = 6, so b = 2. The second equation becomes x^2 + 2x + q = 0, and because it has equal roots, its discriminant must be zero, so 2^2 - 4(1)(q) = 0. Solving 4 - 4q = 0 yields q = 1.

Keep practicing — related questions