TS EAMCET · Maths · Quadratic Equation
If the equations \(x^2+p x+2=0\) and \(x^2+x+2 p=0\) have a common root then the sum of the roots of the equation \(x^2+2 p x+8=0\) is
- A \(-3\)
- B \(3\)
- C \(6\)
- D \(-6\)
Answer & Solution
Correct Answer
(C) \(6\)
Step-by-step Solution
Detailed explanation
\((x^2+p x+2)-(x^2+x+2 p)=0\) \((p-1)x + 2(1-p)=0\) \((p-1)(x-2)=0\) If \(p=1\), \(x^2+x+2=0\) (no real roots). For \(x^2+2px+8=0\), \(x^2+2x+8=0\), sum \(-2\). Common root \(x=2\). \(2^2+p(2)+2=0 \Rightarrow 4+2p+2=0 \Rightarrow 2p=-6 \Rightarrow p=-3\) For \(x^2+2px+8=0\):…
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