TS EAMCET · Maths · Quadratic Equation
If \(x^2-3 a x+14=0\) and \(x^2+2 a x-16=0\) have a common root then \(a^4+a^2=\)
- A 2
- B 90
- C 6
- D 20
Answer & Solution
Correct Answer
(B) 90
Step-by-step Solution
Detailed explanation
We have, \[ x^2-3 a x+14=0 \text { and } x^2+2 a x-16=0 \] Let the common roots is \(\alpha\). Then, \(\alpha^2-3 a \alpha+14=0\) and \(\alpha^2+2 a \alpha-16=0\) by Cramer rule, \[ \frac{\alpha^2}{48 a-28 a}=\frac{\alpha}{14+16}=\frac{1}{2 a+3 a} \]…
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