Question

If `(a^(2)-14a+13)x^(2)+(a+2)x-2=0` does not have two distinct real roots, then the maximum value of `a^(2)-15a` is _________.

Answer 1

Correct Answer - -9
Let `f(x)=(a^(2)-14a+13)x^(2)+(a+2)x-2`
Given that the above equation does not have two distinct real roots.
Therefore, either `f(x)geO or f(x)le O AA x in R`.
But `f(0)=-2lt0`
`therefore f(0)le0AAx in R`
So, `f(-1)le0`
`rArr(a^(2)-14a+13)-(a+2)-2le0`
`rArr a^(2)-15a+9le0`
`rArr a^(2)-15a+9le0`
So, the maximum value of `a^(2)-15a " is "-9`