x^2 + 11x - 3
What two numbers multiply to -3 and add to 11?
Let's use the quadratic equation:
\(x = \frac{-b\pm \sqrt{b^2-4ac}}{2a}\)
Where the equation is ax^2 + bx + c
\(x = \frac{-11\pm \sqrt{11^2-4(1)(-3)}}{2(1)}\\\\x = \frac{-11\pm \sqrt{121+12}}{2}\\\\x = \frac{-11\pm \sqrt{133}}{2}\\\\ \boxed{\bf{x = -\frac{11}{2} + \frac{\sqrt{133}}{2}}}\\\\ \boxed{\bf{x = -\frac{11}{2} - \frac{\sqrt{133}}{2}}}\)
The two boxed values are what multiply to -3 and add to 11.
