How do you find the roots, real and imaginary, of y=-x^2+5x-9 using the quadratic formula?

1 Answer
Johnson Z.
Mar 16, 2016

real roots: none
imaginary roots: x=(5+-sqrt(11)i)/2

Explanation:

Since the given equation is already in standard form, identify the color(blue)a,color(darkorange)b, and color(violet)c values. Then plug the values into the quadratic formula to solve for the roots.

y=color(blue)(-1)x^2 color(darkorange)(+5)x color(violet)(-9)

color(blue)(a=-1)color(white)(XXXXX)color(darkorange)(b=5)color(white)(XXXXX)color(violet)(c=-9)

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

x=(-(color(darkorange)(5))+-sqrt((color(darkorange)(5))^2-4(color(blue)(-1))(color(violet)(-9))))/(2(color(blue)(-1)))

x=(-5+-sqrt(25-36))/-2

x=(-5+-sqrt(-11))/-2

x=(-(-5+sqrt(11)i))/2color(white)(X),color(white)(X)(-(-5-sqrt(11)i))/2

x=(5-sqrt(11)i)/2color(white)(X),color(white)(X)(5+sqrt(11)i)/2

color(green)(|bar(ul(color(white)(a/a)x=(5+-sqrt(11)i)/2color(white)(a/a)|)))

:., the imaginary roots are x=(5+-sqrt(11)i)/2.

Related questions
See all questions in Quadratic Formula
Impact of this question
2047 views around the world
You can reuse this answer
Creative Commons License