AP EAMCET · Maths · Quadratic Equation
If \(3 x^2-7 x+2=0\) and \(15 x^2-11 x+a=0\) have a common root and \(a\) is a positive real number, then the sum of the roots of the equation \(15 x^2-a x+7=0\), is
- A \(\frac{76}{15}\)
- B \(\frac{38}{15}\)
- C \(\frac{2}{15}\)
- D \(\frac{36}{15}\)
Answer & Solution
Correct Answer
(C) \(\frac{2}{15}\)
Step-by-step Solution
Detailed explanation
Given equations are \(\text { and } \begin{aligned} 3 x^2-7 x+2 & =0 \\ 15 x^2-11 x+a & =0 \\ \text { Here, } \quad a_1=3, b_1=-7, c_1 & =2 \\ a_2=15, b_2=-11, c_2 & =a \end{aligned}\) and Let \(\alpha\) is a common root of the Eqs. (i) and (ii), Then, \(\alpha\) will satisfy…
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