Find the value of p for which the quadratic equation 2x2 + px + 8 = 0�

1.	Find the value of p for which the quadratic equation 2x2 + px + 8 = 0 has real roots.
Answer» Given: 2x²+ px + 8 = 0 Here a = 2, b = p and c = 8 Discriminant D is given by: D = (b² - 4ac) = p² - 4 x 2 x 8 = (p² - 64) If D ≥ 0, the roots of the equation will be real ⇒ (p² - 64) ≥ 0 ⇒ (p + 8) (p - 8) ≥ 0 ⇒ p ≥ 8 and p ≤ - 8 Thus, the roots of the equation are real for p ≥ 8 and p ≤ - 8.

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

Answer»

Given:

2x²+ px + 8 = 0

Here

a = 2, b = p and c = 8

Discriminant D is given by:

D = (b² - 4ac)

= p² - 4 x 2 x 8

= (p² - 64)

If D ≥ 0, the roots of the equation will be real

⇒ (p² - 64) ≥ 0

⇒ (p + 8) (p - 8) ≥ 0

⇒ p ≥ 8 and p ≤ - 8

Thus, the roots of the equation are real for p ≥ 8 and p ≤ - 8.