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Algebra Level 3

If $(x-3)(x-4) = \Large\frac{34}{33^{2}}$ and $S$ is the sum of all possible values of $x$ then find the digital root of $33S$ .

No such values of 8 6 4 9

1 solution

Akshat Sharda
Jul 4, 2015

As you can see , $x= \frac{133}{33}$ and $\frac{98}{33}$ Therefore , Sum of possible values of $x$

$S$ =

= $\frac{133}{33} + \frac{98}{33}$

= $\frac{133+98}{33}$

= $\frac{231}{33}$

Therefore ,

Digital rool of $33S =$

= $33× \frac{231}{33}$

= $231$ = $2+3+1$ = $\boxed{6}$

just use vieta

Dev Sharma - 5 years, 7 months ago

What would have happened If I change the question?

Will you be able to calculate its roots easily?

Akshat Sharda - 5 years, 7 months ago