JEE Mains · Maths · STD 11 - 4.2 Quadratic equations and inequations
Let \(p(x)\) be a quadratic polynomial such that \(p(0)= 1\) . If \(p(x)\) leaves remainder \(4\) when divided by \(x-1\) and it leaves remainder \(6\) when divided by \(x+ 1\) ; then
- A \(p(b) = 11\)
- B \(p(b) = 19\)
- C \(p(-2) = 19\)
- D \(p(-2) = 11\)
Answer & Solution
Correct Answer
(C) \(p(-2) = 19\)
Step-by-step Solution
Detailed explanation
\((c)\) Let \(p(x)=a x^{2}+b x+c\) \(\because p(0)=1 \Rightarrow c=1\) \(\text { Also, } p(1)=4\,\, \,p(-1)=6\) \(\Rightarrow a+b+1=4\,\, \,a-b+1=6\) \(\Rightarrow a+b=3 \,\,\, a-b=5\) \(\Rightarrow a=4 \,\,\, b=-1\) \({p(x) = 4{x^2} - x + 1}\) \({p(2) = 16 - 2 + 1 = 15}\)…
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