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

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Answer 1 · 2017-06-13T04:24:57

#x approx 5.54138 or approx -0.54138#

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]}