[tex]Option\ C\\\\\mathrm{The\:solutions\:to\:the\:quadratic\:equation\:are:} x=16,\:x=-3[/tex]
Solution:
[tex]\text{ Given that, }[/tex]
[tex]x^2 - 13x - 48 = 0[/tex]
[tex]\text{We have to solve using Quadratic Formula }[/tex]
[tex]\mathrm{For\:a\:quadratic\:equation\:of\:the\:form\:}ax^2+bx+c=0\mathrm{\:the\:solutions\:are\:}\\\\x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
[tex]\text{ From given,}[/tex]
[tex]x^2 - 13x - 48 = 0[/tex]
[tex]\mathrm{For\:}\quad a=1,\:b=-13,\:c=-48[/tex]
[tex]x =\frac{-\left(-13\right)\pm \sqrt{\left(-13\right)^2-4\cdot \:1\left(-48\right)}}{2\cdot \:1}\\\\Simplify\\\\x = \frac{13 \pm \sqrt{\left(-13\right)^2+4\cdot \:1\cdot \:48}}{2\cdot \:1}\\\\x = \frac{13 \pm \sqrt{361}}{2}[/tex]
[tex]Simplify\\\\x = \frac{ 13 \pm 19 }{2}\\\\We\ have\ two\ solutions\\\\x = \frac{13+19}{2}\\\\x = 16\\\\And\\\\x = \frac{13-19}{2}\\\\x = -3[/tex]
[tex]\mathrm{The\:solutions\:to\:the\:quadratic\:equation\:are:} x=16,\:x=-3[/tex]
