Question

If α and β are roots of the equation x²+px+(3p)/(4)=0, such that |α-β|=√(10), then p belongs to the set

• A. 2,-5
• B. -3,2
• C. -2,5
• D. 3,-5

Hint:

For quadratic roots: (α-β)²=(α+β)²-4αβ is often faster than using the discriminant.

Answer 1

The Correct Option is C

Step 1: For a quadratic x²+px+(3p)/(4)=0: α+β=-p, αβ=(3p)/(4) Step 2: Use: (α-β)²=(α+β)²-4αβ (α-β)²=p²-3p Step 3: Given |α-β|=√(10): p²-3p=10 ⟹ p²-3p-10=0 Step 4: Solving: (p-5)(p+2)=0 ⟹ p=5,-2 ⟹ p∈-2,5