WBJEE · Maths · Quadratic Equation
The quadratic equation whose roots are three times the roots of \(3 a x^2+3 b x+c=0\) is
- A \(a x^2+3 b x+3 c=0\)
- B \(\mathrm{ax}^2+3 \mathrm{bx}+\mathrm{c}=0\)
- C \(9 a x^2+9 b x+c=0\)
- D \(a x^2+b x+3 c=0\)
Answer & Solution
Correct Answer
(A) \(a x^2+3 b x+3 c=0\)
Step-by-step Solution
Detailed explanation
Hints: \(3 a \alpha^2+3 b \alpha+c=0\) \[ x=3 \alpha \Rightarrow \alpha=\frac{x}{3} \] \[ \begin{aligned} & 3 a \frac{x^2}{9}+3 b \cdot \frac{x}{3}+c=0 \\ & a x^2+3 b x+3 c=0 \end{aligned} \]
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