WBJEE · Maths · Quadratic Equation
If \(\sin \theta\) and \(\cos \theta\) are the roots of the equation \(a x^2-b x+c=0\), then \(\mathrm{a}, \mathrm{b}\) and \(\mathrm{c}\) satisfy the relation
- A \(a^2+b^2+2 a c=0\)
- B \(\mathrm{a}^2-\mathrm{b}^2+2 \mathrm{ac}=0\)
- C \(\mathrm{a}^2+\mathrm{c}^2+2 \mathrm{ab}=0\)
- D \(\mathrm{a}^2-\mathrm{b}^2-2 \mathrm{ac}=0\)
Answer & Solution
Correct Answer
(B) \(\mathrm{a}^2-\mathrm{b}^2+2 \mathrm{ac}=0\)
Step-by-step Solution
Detailed explanation
Hints: \(\sin \theta+\cos \theta=\frac{b}{a}\) \(\begin{aligned} & \sin \theta \cdot \cos \theta=\frac{c}{a} \\ & \left(\frac{b}{a}\right)^2=1+\frac{2 c}{a} \\ & b^2=a^2+2 a c \\ & a^2-b^2+2 a c=0 \end{aligned}\)
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