| Case Study : Q. 31 to 35 |
| A group of school friends went on an expedition to see caves. One person remarked that the entrance of the caves resembles a parabola, and can be represented by a quadratic polynomial \[f(x)=a{{x}^{2}}+bx+c,\] \[a\ne 0,\] where a, b and c are real numbers. |
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| Based on the above information give the answer of the following questions. |
A) \[\frac{3}{5}\]
B) \[\frac{3}{4}\]
C) \[\frac{2}{5}\]
D) \[\frac{1}{5}\]
Correct Answer: B
Solution :
| Since, \[x=4\]is one of the zero of the polynomial \[(p-1){{x}^{2}}+px+1\]then |
| \[(p-1)\,\,{{(4)}^{2}}+p(4)+1=0\] |
| \[\Rightarrow \,\,\,\,\,\,\,\,\,16p-16+4p+1=0\] |
| \[\Rightarrow \,\,\,\,\,\,\,\,\,20p=15\Rightarrow p=\frac{3}{4}\] |
| So, option [b] is correct. |
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