# Find the values of p for which the quadratic equation 2x2 + px + 8 = 0 has real roots.

Given that the quadratic equation 2x2 + px + 8 = 0 has real roots

Comparing with standard quadratic equation ax2 + bx + c = 0

a = 2 b = p c = 8

Thus D = 0

Discriminant D = b2 – 4ac≥0

(p)2 – 4.2.8≥0

(p)2 – 64≥0

p2 ≥ 64 taking square root on both sides

p≥8 or p≤ – 8

The roots of equation are real for p≥8 or p≤ – 8

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