If 3x 2 – ax + 6 = ax 2 + 2x + 2 has only one (repeated) solution
| If 3x2 – ax + 6 = ax2 + 2x + 2 has only one (repeated) solution, then the positive integral solution of a is:
A. 3
B. 2
C. 4
D. 5
Please scroll down to see the correct answer and solution guide.
Right Answer is: B
SOLUTION
Given equation is 3x2 – ax + 6 = ax2 + 2x + 2
⇒ 3x2 – ax2 – ax – 2x + 6 – 2 = 0
⇒ (3 – a)x2 – (a + 2)x + 4 = 0
As the equation has only (one repeated solution)
⇒ D = B2 – 4AC = 0
⇒ (a + 2)2 – 4(3 – a)4 = 0
⇒ a2 + 4a + 4 – 48 + 16a = 0
⇒ a2 + 20a – 44 = 0
⇒ a2 + 22a – 2a – 44 = 0
⇒ a(a + 22) – 2(a + 22) = 0
⇒ a = 2, -22
∴ Positive integral solution of a = 2