How do you find the roots, real and imaginary, of #y= 5x^2 - 2x-45 # using the quadratic formula?

1 Answer

Answer:

Since #b^2-4ac# is 904 which is a positive number, the given quadratic equation has real roots.

#x=(2+-sqrt904)/10#

Explanation:

When the quadratic equation is in the form -

#ax^2+bx+c=0#

Then its roots are given by

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

In this #b^2-4ac# determines whether a given equation has real roots or imaginary roots.

If #b^2-4ac# is positive the roots are positive.

If #b^2-4ac# is negative the roots are negative.

In our case -

#(-2)^2-(4xx5xx-45)#
#4 - (-900)#
#4+900=904#

Since #b^2-4ac# is 904 which is a positive number, the given quadratic equation has real roots. So we should be able to plug into the quadratic formula without having imaginary numbers:

#x=(2+-sqrt(904))/(2(5))#

#x=(2+-sqrt904)/10#