JEE Mains · Maths · STD 12 - 6. Application of derivatives
Let \(a\) be an integer such that all the real roots of the polynomial \(2 x^{5}+5 x^{4}+10 x^{3}+10 x^{2}+10 x+10\) lie in the interval \((a, a+1) .\) Then, \(| a |\) is equal to ...... .
- A \(1\)
- B \(2\)
- C \(4\)
- D \(3\)
Answer & Solution
Correct Answer
(B) \(2\)
Step-by-step Solution
Detailed explanation
Let \(2 x^{5}+5 x^{4}+10 x^{3}+10 x^{2}+10 x+10=f(x)\) Now \(f(-2)=-34\) and \(f(-1)=3\) Hence \(f(x)\) has a root in \((-2,-1)\) Further \(f^{\prime}(x)=10 x^{4}+20 x^{3}+20 x^{2}+20 x+10\)…
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