JEE Mains · Maths · STD 11 - 4.2 Quadratic equations and inequations
If the two roots of the equation \(\left( {a - 1} \right)\left( {{x^4} + {x^2} + 1} \right) + \left( {a + 1} \right){\left( {{x^2} + x + 1} \right)^2} = 0\) are real and distinct, then the set of all values of \('a'\) is
- A \(\left( {0\,,\,\frac{1}{2}} \right)\)
- B \(\left( {\, - \frac{1}{2}\,,\,0} \right) \cup \left( {0\,,\,\frac{1}{2}} \right)\)
- C \(\left( {\, - \frac{1}{2}\,,\,0} \right)\)
- D \(\left( { - \infty \,,\, - 2} \right) \cup \left( {2\,,\,\infty } \right)\)
Answer & Solution
Correct Answer
(B) \(\left( {\, - \frac{1}{2}\,,\,0} \right) \cup \left( {0\,,\,\frac{1}{2}} \right)\)
Step-by-step Solution
Detailed explanation
\((a-1)\left(x^{4}+x^{2}+1\right)\) \(+(a+1)\left(x^{2}+x+1\right)^{2}=0\) \(\Rightarrow(a-1)\left(x^{2}+x+1\right)\left(x^{2}-x+1\right)\) \(+(a+1)\left(x^{2}+x+1\right)^{2}=0\) \( \Rightarrow \left( {{x^2} + x + 1} \right)[(a - 1)\left( {{x^2} - x + 1} \right)\)…
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