Question

The quadratic equation $x^2-1088x+295680=0$ has two positive integral roots whose greater common divisor is $16$. The least common multiple of the roots is

• A. $18240$
• B. $18480$
• C. $18960$
• D. $19240$

Answer 1

The correct option is B $18480$

$\begin{array}{c}{x}^2-1088x+295680=0\\ x=\frac{-\left(-1088\right)\pm \sqrt{{\left(1088\right)}^2-4\times 295680}}{2\times 1}\\ =\frac{1088\pm \sqrt{1183744-1182720}}{2}\\ =\frac{1088\pm \sqrt{1024}}{2}\\ =\frac{1088\pm 32}{2}\\ x=\frac{1088+32}{2},\frac{1088-32}{2}\\ =\frac{1120}{2},\frac{1056}{2}\\ =560,528\end{array}$

Least common multiply of root -

$\begin{array}{c}=\frac{560\times 528}{2}\\ =18480.\end{array}$