Question

How do you use the quadratic formula to solve for x-intercepts `x^2 − 5x − 3 = 0`?

Answer 1

`x approx 5.54138 or approx -0.54138`

Explanation:

The quadratic formula states that for a quadratic equation of standard form `(ax^2+bx+c=0)` it's roots are given by:

`x = (-b+-sqrt(b^2-4ac))/(2a)`

In this example we are asked to find the x-intercepts (which are the roots) of `x^2-5x-3 =0`

`:. a=1, b=-5, c=-3`

Hence `x= (-(-5)+-sqrt((-5)^2-4*1*(-3)))/(2*1)`

`= (5+-sqrt(25+12))/2`

`= (5+-sqrt(37))/2`

`x approx 5.54138 or approx -0.54138`

These x-intercepts can be seen on the graph of this quadratic below

graph{x^2-5x-3 [-18.14, 22.4, -9.91, 10.36]}