Question

If the quadratic equations ax² + 2cx + b = 0 and ax² + 2bx + c = 0 (b ¹ c) have a common root, then a + 4 b + 4c is ;

• A. – 2
• B. – 1
• C. 0
• D. 1

Answer 1

Answer: (C)

0

Answer 2

Let a be common root, then

$\frac{\begin{aligned} & a\alpha^{2} + 2c\alpha + b = 0 \\ & a\alpha^{2} + 2b\alpha + c = 0 \end{aligned}}{2(c–b)\alpha = c–b \Rightarrow \alpha = 1/2}$

putting a = 1/2 in aa² + 2ca + b = 0, we get a + 4b + 4c = 0