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

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justaguide | Certified Educator

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)`