Question

what are the zeros of f(x)=x^2-2x-3

Answer 1

The zeros are x = 3 and x = -1

Solution:

Given that,

$f(x) = x^2 -2x-3$

We have to find the zeros of above quadratic function

$\mathrm{Solve\:with\:the\:quadratic\:formula}\\\\\mathrm{For\:a\:quadratic\:equation\:of\:the\:form\:}ax^2+bx+c=0\mathrm{\:the\:solutions\:are\:}\\\\x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

$\mathrm{For\:}\quad a=1,\:b=-2,\:c=-3\\\\\quad x=\frac{-\left(-2\right)\pm \sqrt{\left(-2\right)^2-4\cdot \:1\left(-3\right)}}{2\cdot \:1}\\\\Simplify\\\\x = \frac{2 \pm \sqrt{4 + 12}}{2}\\\\x = \frac{2 \pm \sqrt{16}}{2}\\\\x = \frac{2 \pm 4}{2}\\\\x = 1 \pm 2\\\\Thus\ we\ have\ two\ solutions\\\\x = 1 + 2 = 3\\\\x = 1 -2 = -1$

Thus the zeros are x = 3 and x = -1