TS EAMCET · Maths · Quadratic Equation
The equations \(2 x^2+a x-2=0\) and \(x^2+x+2 a=0\) have exactly one common root. If \(a \neq 0\), then one of the roots of the equation \(a x^2-4 x-2 a=0\) is
- A 2
- B -2
- C \(\frac{-4+\sqrt{22}}{3}\)
- D \(\frac{-2+\sqrt{22}}{3}\)
Answer & Solution
Correct Answer
(D) \(\frac{-2+\sqrt{22}}{3}\)
Step-by-step Solution
Detailed explanation
We know that condition of exactly one common root of quadratic equations \(a_1 x^2+b_1 x+c_1=0\) and \(a_2 x^2+b_2 x+c_2=0\) is \(\left(c_1 a_2-c_2 a_1\right)^2=\left(b_1 c_2-b_2 c_1\right)\left(a_1 b_2-a_2 b_1\right)\) Here, \(a_1=2, b_1=a, c_1=-2, a_2=1, b_2=1\) and…
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