How do you use the discriminant to determine the numbers of solutions of the quadratic equation #x^2 + 6x - 7 = 0# and whether the solutions are real or complex?

1 Answer
Tony B
Feb 5, 2016

see explanantion

Explanation:

Consider the following value for the discriminant: (d)

#d>0 ->#The plot crosses the x-axis so has 2 solutions

#d=0->#The plot is such that it does not cross the x-axis but the#" "# axis forms a tangent to the max/min

#d<0->#The plot does not cross nor come into contact with the #" "#x-axis. Thus any solution to the expression being #" "#equated to zero will result in a complex number solution.

For your equation of: #x^2+6x-7=0#
Tony B

The discriminant is:

#sqrt(b^2-4ac) -> sqrt(6^2-4(1)(-7))#

#sqrt(6^2+28)" ">" "0" " =>" " 2" solutions"#

As these are not complex they are real solutions

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