If ax2 + bx + c = a (x – p)2 , then the relation among

Home » Aptitude » Algebra » Question

If ax² + bx + c = a (x – p)² , then the relation among a, b, c would be

1. abc = 1
2. b² = ac
3. b² = 4ac
4. 2b = a + c

Correct Option: C

ax² + bx + c = a (x – p)²
⇒ ax² + bx + c = a (x² – 2px + p²)
⇒ ax² + bx + c = ax² – 2apx + ap²
Comparing the corresponding coefficients,
b = – 2ap and c = ap²

⇒ b² = 4a²p² and p² =	c
	a

⇒ p² =	b²	;
	4a²

∴	b² =	=	c	⇒ b² = 4ac
	4a²		a