JEE Mains · Maths · STD 11 - 4.2 Quadratic equations and inequations
The number of distinct real roots of the equation \(x^{5}\left(x^{3}-x^{2}-x+1\right)+x\left(3 x^{3}-4 x^{2}-2 x+4\right)-1=0\) is
- A \(8\)
- B \(3\)
- C \(5\)
- D \(0\)
Answer & Solution
Correct Answer
(B) \(3\)
Step-by-step Solution
Detailed explanation
\(x ^{5}\left( x ^{3}- x ^{2}- x +1\right)+ x \left(3 x ^{3}-4 x ^{2}-2 x +4\right)-1=0\) \(( x -1)^{2}( x +1)\left( x ^{5}+3 x -1\right)=0\) Let \(f(x)=x^{5}+3 x-1\) \(f^{\prime}(x)>0 \forall x \in R\) Hence \(3\) real distinct roots.
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