JEE Mains · Maths · STD 11 - 4.2 Quadratic equations and inequations
The equation \(\sqrt {3 {x^2} + x + 5} = x - 3\) , where \(x\) is real, has
- A no solution
- B exactly one solution
- C exactly two solution
- D exactly four solution
Answer & Solution
Correct Answer
(A) no solution
Step-by-step Solution
Detailed explanation
Consider \(\sqrt{3 x^{2}+x+5}=x-3\) Squaring both the sides, we get \(3 x^{2}+x+5=(x-3)^{2}\) \(\Rightarrow 3 x^{2}+x+5=x^{2}+9-6 x\) \(\Rightarrow 2 x^{2}+7 x-4=0\) \(\Rightarrow 2 x^{2}+8 x-x-4=0\) \(\Rightarrow 2 x(x+4)-1(x+4)=0\) \(\Rightarrow x=\frac{1}{2}\) or \(x=-4\) For…
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