AP EAMCET · Maths · Quadratic Equation
The number of real roots of the equation \(x^5+3 x^3+4 x+30=0\) is
- A \(1\)
- B \(2\)
- C \(3\)
- D \(5\)
Answer & Solution
Correct Answer
(A) \(1\)
Step-by-step Solution
Detailed explanation
Let \(f(x)=x^5+3 x^3+4 x+30\) \(\Rightarrow f^{\prime}(x)=5 x^4+9 x^2+4\) As \(f^{\prime}(x)\) consist of the terms which has even powers of \(x\). \(f^{\prime}(x)>0\) for all \(x \in \mathrm{R}\) Hence, the \(f(x)=0\) has only one real root.
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