WBJEE · Maths · Quadratic Equation
If the quadratic equation \(a x^2+b x+c=0(a\gt0)\) has two roots \(\alpha\) and \(\beta\) such that \(\alpha \lt -2\) and \(\beta\gt2\) then
- A \(\mathrm{c} \lt 0\)
- B \(a+b+c\gt0\)
- C \(a-b+c \lt 0\)
- D \(a-b+c\gt0\)
Answer & Solution
Correct Answer
(C) \(a-b+c \lt 0\)
Step-by-step Solution
Detailed explanation
Hint: \(f(x)=a x^2+b x+c\) so, \(f(-2) \lt 0\) and \(f(2)\gt0\) also, \(f(0) \lt 0 \Rightarrow c \lt 0\) \(\begin{aligned} & f(-1) \lt 0 \Rightarrow a-b+c \lt 0 \\ & f(1) \lt 0 \Rightarrow a+b+c \lt 0 \end{aligned}\)
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