Question

find p. 2x²+px+8=0 has two distinct real roots​

Answer 1

Answer:

The set of values of p is p ∈ [ 8, ∞ ).

Step-by-step-explanation:

The given quadratic equation is 2x² + px + 8 = 0.

We have given that the equation has two distinct real roots.

We have to find the value of p.

Comparing given equation with ax² + bx + c = 0, we get,

• a = 2
• b = p
• c = 8

For real and distinct roots,

b² - 4ac ≥ 0

⇒ p² - 4 * 2 * 8 ≥ 0

⇒ p² - 8 * 8 ≥ 0

⇒ p² ≥ 8 * 8

⇒ p ≥ √( 8 * 8 )

⇒ p ≥ 8

Thus, p is equal to 8 and equal to any real number greater than 8.

∴ The set of values of p is p ∈ [ 8, ∞ ).