1.

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

Answer»

2x2 + px + 8 = 0

Compare given equation with the general form of quadratic equation, which is ax2 + bx + c = 0

a = 2, b = p, c = 8

Find D:

D = b2 – 4ac

= p2 – 4 x 2 x 8

= p2 – 64

Since roots are real, so D ≥ 0

p2 – 64 ≥ 0

p2 ≥ 64

≥ (±8)2

Either p ≥ 8 or p ≤ -8



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