The roots of the equation ax 2 + ( 4a 2 - 3b )x

Home » Aptitude » Quadratic Equation » Question

The roots of the equation ax² + ( 4a² - 3b )x - 12ab = 0 are

1. 4a , 3b
  a
2. 4a , - 3b
  a
3. - 4a , 3b
  a
4. - 4a , - 3b
  a

Correct Option: C

Let k₁ and k₂ be the roots of given quadratic equation .
The given quadratic equation is
ax² + ( 4a² - 3b )x - 12ab = 0
⇒ ax² + 4a²x - 3bx - 12ab = 0
⇒ ax ( x + 4a ) - 3b ( x + 4a ) = 0
⇒ ( x + 4a ) ( ax - 3b ) = 0
⇒ ax - 3b = 0 or x + 4a = 0

⇒ x =	3b	or x = - 4a
	a

Thus, the two roots of the given quadratic equation are

- 4a	and	3b
		a