How do you solve r^2+25=0 using the quadratic formula?

1 Answer
Alan P.
Dec 3, 2016

r=-5i or r=+5i

Explanation:

The quadratic formula tells us that a quadratic in standard form:
color(white)("XXX")color(red)ax^2+color(blue)bx+color(green)c=0
has solutions given by:
color(white)("XXX")x=(-color(blue)b+-sqrt(color(blue)b^2-4color(red)acolor(green)c))/(2color(red)a)

Converting the given: r^2+25=0 into standard form:
color(white)("XXX")color(red)1r^2+color(blue)0r+color(green)(25)=0
we have the solutions:
color(white)("XXX")r=(color(blue)0+-sqrt(color(blue)0^2-4*color(red)1*color(green)(25)))/(2*color(red)1)

color(white)("XXX")=+-(2sqrt(-25))/2 = +-sqrt(-25) = +-5i

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