WBJEE · Maths · Quadratic Equation
For all real values of \(a_{0}, a_{1}, a_{2}, a_{3}\) satisfying \(a_{0}+\frac{a_{1}}{2}+\frac{a_{z}}{3}+\frac{a_{3}}{4}=0,\) the equation \(a_{0}+a_{1} x+a_{2} x^{2}+a_{3} x^{3}=0\) has a real root in the interval
- A [0,1]
- B [-1,0]
- C [1,2]
- D [-2,-1]
Answer & Solution
Correct Answer
(A) [0,1]
Step-by-step Solution
Detailed explanation
Let \(f(x)=\frac{a_{3} x^{4}}{4}+\frac{a_{2} x^{3}}{3}+\frac{a_{1} x^{2}}{2}+a_{0} x\) \(f(0)=0, f(1)=\frac{a_{3}}{4}+\frac{a_{2}}{3}+\frac{a_{1}}{2}+a_{0}=0\) \(\Rightarrow f(0)=f(1)\) \(\Rightarrow f^{\prime}(x)=0\) has atleast one real root in |0,1|…
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