AP EAMCET · Maths · Quadratic Equation
If the values of \(k\) for which the equation \(x^2+2(k+2) x+\) \(6 \mathrm{k}+7=0\) has equal roots are \(\mathrm{k}_1\) and \(\mathrm{k}_2\), then \(\mathrm{k}_1^2+\mathrm{k}_2^2=\)
- A 8
- B 9
- C 10
- D 12
Answer & Solution
Correct Answer
(C) 10
Step-by-step Solution
Detailed explanation
\(x^2+2(k+2) x+6 k+7=0\) has equal roots Hence \[ \begin{aligned} & b^2-4 a c=0 \\ & \left.\Rightarrow[2(k+2)]^2-4(1)(6 \mathrm{k}+7)\right]=0 \\ & \Rightarrow k=3,1 \end{aligned} \] Hence \(k_1=3, k_2=1\) \[ \therefore \quad k_1^2+k_2^2=10 \]
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