TS EAMCET · Maths · Functions
\(f(x)=a x^2+b x+c\) is an even function and \(g(x)=p x^3+q x^2+r x\) is an odd function. If \(h(x)=f(x)+g(x)\) and \(h(-2)=0\), then \(8 p+4 q+2 r=\)
- A \(4 a+3 b+2 c\)
- B \(a+b+c\)
- C \(4 a+2 b+c\)
- D \(8 a+4 b+2 c\)
Answer & Solution
Correct Answer
(C) \(4 a+2 b+c\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \text { } f(x)=f(-x) \\ & a x^2+b x+c=a x^2-b x+c \Rightarrow b=0 \\ & g(x)+g(-x)=0 \Rightarrow q=0 \\ & h(x)=p x^3+q x^2+a x^2+b x+r x+c \\ & \text { and } h(-2)=0 \\ & \Rightarrow-8 p+4 q+4 a-2 r-2 b+c=0 \\ & \Rightarrow-8 p+4 a-2 r+c=0 \\ & \Rightarrow 8 p+2…
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