AP EAMCET · Maths · Quadratic Equation
If \(x^2+5 a x+6=0\) and \(x^2+3 a x+2=0\) have a common root then that common root is
- A 3 (or) -3
- B 2 (or) -2
- C 2 (or) -3
- D -2 (or) 3
Answer & Solution
Correct Answer
(B) 2 (or) -2
Step-by-step Solution
Detailed explanation
Let \(y\) be a common root of \(x^2+5 a x+6=0\) and \(x^2+3 a x+2=0\) So, \(y^2+5 a y+6=0\) and \(y^2+3 a y+2=0\) \(\Rightarrow 5 a y+6=3 a y+2 \Rightarrow 2 a y=-4 \Rightarrow a y=-2\) So, \(y^2+5 \cdot(-2)+6=0 \Rightarrow y^2-4=0 \Rightarrow y= \pm 2\).
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