| (i) One of them made a mistake in the constant term and got the roots as 5 I and 9. |
| (ii) Another one committed an error in the coefficient of x and he got the roots as 12 and 4. |
A) \[{{x}^{2}}+4x+14=0\]
B) \[2{{x}^{2}}+7x-24=0\]
C) \[{{x}^{2}}\text{-}14x+48=0\]
D) \[3{{x}^{2}}-17x+52=0\]
Correct Answer: C
Solution :
For 1st one, Let the equation be \[{{x}^{2}}+ax+b=0\] Since roots are 5 and 9 \[\therefore \] \[a=-14\]and \[b=45\] For 2nd one, Let the equation be \[{{x}^{2}}+px+q=0\] Since roots are 12 and 4. \[p=-16\]and \[q=48\] Now, according to the question, b and p both are wrong. Therefore, the correct equation would be \[{{x}^{2}}-14x+48=0\]
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