AP EAMCET · Maths · Quadratic Equation
\(E_1: a+b+c=0, \quad\) if 1 is a root of \(a x^2+b x+c=0, \quad E_2: b^2-a^2=2 a c\), if \(\sin \theta\), \(\cos \theta\) are the roots of \(a x^2+b x+c=0\) Which of the following is true?
- A \(E_1\) is true, \(E_2\) is true
- B \(E_1\) is true, \(E_2\) is false
- C \(E_1\) is false, \(E_2\) is true
- D \(E_1\) is false, \(E_2\) is false
Answer & Solution
Correct Answer
(A) \(E_1\) is true, \(E_2\) is true
Step-by-step Solution
Detailed explanation
Given that, 1 is a root of \(a x^2+b x+c=0\) \(\begin{aligned} & \Rightarrow \quad a+b+c=0 \\ & \therefore \quad E_1: a+b+c=0 \text { is true. } \end{aligned}\) Since \(\cos \theta, \sin \theta\) are the roots of…
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\[
\triangle A B C, \frac{(a+b+c)(b+c-a)(c+a-b)(a+b-c)}{4 b^2 c^2}
\]
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