Question

What are the roots of the equation x^2-9x-10?

(a) 9, 1

(b) -9, -1

(c) -10, 1

(d) 10, -1

This question was addressed to me in an interview for job.

The above asked question is from Solution of Quadratic Equation by Squaring Method topic in chapter Quadratic Equation of Mathematics – Class 10

Answer 1

The correct choice is (d) 10, -1

The best explanation: x^2-9x-10=0

Shifting -10 to RHS

x^2-9x=10

Adding \(\frac {b^2}{4}\) on both sides, where b=-9

x^2 – 9x + \(\frac {-9^2}{4} = \frac {-9^2}{4}\) + 10

x^2 – 9x + \(\frac {81}{4} = \frac {81}{4}\) + 10

x^2 – 9x + \(\frac {81}{4} = \frac {121}{4}\)

\((x-\frac {9}{2})\)^2=\((\frac {11}{2})\)^2

x – \(\frac {9}{2}\) = ± \(\frac {11}{2}\)

x = \(\frac {11}{2}+\frac {9}{2}=\frac {20}{2}\) = 10 and x = \(\frac {-11}{2} + \frac {9}{2} = \frac {-2}{2}\) = -1

The roots of the equation are 10 and -1.