Solve for values of b such that the equation 2x^2 - bx + 8 = 0 has real roots.

1 Answer | Add Yours

justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

The roots of a quadratic equation ax^2 + bx + c = 0 are real if `b^2 - 4ac >= 0` .

The equation 2x^2 - bx + 8 = 0 has real roots if `(-b)^2 - 4*2*8 >= 0`

=> `b^2 >= 64`

=> `b >= 8` or `b <= -8`

The equation 2x^2 - bx + 8 = 0 has real roots for values of b that lie in the set `(-oo, -8]U[8, oo)`

We’ve answered 318,929 questions. We can answer yours, too.

Ask a question