TS EAMCET · Maths · Quadratic Equation
Let the equations \(a x^2-7 x+c=0\) and \(a x^2+5 x-c=0\) have a common root and \(a c \neq 0\). If 3 is a root of \(a x^2-7 x+c=0\) other than the common root, then the common root of the given equations is
- A 3
- B \(\frac{1}{2}\)
- C 2
- D \(\frac{1}{3}\)
Answer & Solution
Correct Answer
(B) \(\frac{1}{2}\)
Step-by-step Solution
Detailed explanation
\[ \begin{aligned} & \text a x^2-7 x+c=0 \\ & a x^2+5 x-c=0 \end{aligned} \] Let common root be \(\alpha\) \[ \begin{aligned} & a \alpha^2-7 \alpha+c=0 \\ & a \alpha^2+5 \alpha-c=0 \\ & \frac{\alpha^2}{7 c-5 c}=\frac{\alpha}{a c+a c}=\frac{1}{5 a+7 a} \end{aligned} \]…
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