A) \[\frac{3}{16}\left( {{x}^{2}}-6x+16 \right)\]
B) \[\frac{3}{25}\left( {{x}^{2}}-6x+9 \right)\]
C) \[\frac{3}{25}\left( {{x}^{2}}-6x+16 \right)\]
D) \[\frac{3}{16}\left( {{x}^{2}}-6x+9 \right)\]
Correct Answer: B
Solution :
| Let \[f\left( x \right)=a{{x}^{2}}+bx+c\]as it touches X-axis at \[x=3\] |
| \[\Rightarrow \frac{-b}{2a}=3\Rightarrow b=-6a..(1)\] |
| \[\operatorname{Also},\,9a+3b+c=0..\left( 2 \right)\] |
| \[4a-2b+c=3..(3)\] |
| \[\Rightarrow a=\frac{3}{25},b=\frac{18}{25},c=\frac{27}{25}\] |
| \[\Rightarrow f\left( x \right)=\frac{3}{25}\left( {{x}^{2}}-6x+9 \right)\] |
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