Question

2x² + px + 2 = 0 have real roots​

Answer 1

Answer:

the value of p is either 4 or -4

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Answer 2

Answer:

• The value of p is ≥4 or ≥-4

Step-by-step explanation:

Question:

• If the quadratic equation, 2x²+px+2 = 0 have real roots, then find the value of p.

Given that:

• 2x²+px+2 = 0 have real roots​

To find:

• The value of p

As the nature of roots are real, there are two cases:

• Discriminant is greater than 0
• Discriminant = 0

In general, we can write that:

• D ≥ 0

In the following equation,

• b = p
• a = 2
• c = 2

Applying Discriminant Formula:

$\:\:$⇒D = b²-4ac ≥ 0

$\:\:$⇒p²-4×2×2 ≥ 0

$\:\:$⇒p²-16 ≥ 0

$\:\:$⇒p² ≥ 16

$\:\:$⇒p ≥ √16

$\:\:$⇒p ≥ ±4

Final Answer:

• The value of p is ≥4 or ≥-4