A) \[k({{x}^{2}}-2x-8)\]
B) \[k({{x}^{2}}+2x-8)\]
C) \[k({{x}^{2}}+2x+8)\]
D) \[k({{x}^{2}}-2x+8)\]
Correct Answer: A
Solution :
The graph cut x-axis in the above graph at points \[-2\] and 4 which are the zeroes of the graph. |
Now, the required polynomial |
\[=k[{{x}^{2}}-(\text{sum of zeroes})x+\text{product of zeroes}]\] |
\[=k[{{x}^{2}}-(-2+4)x+(-2\times 4)]=k({{x}^{2}}-2x-8)\] |
where, k is an arbitrary constant. |
So, option [a] is correct. |
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