How do you find the discriminant, describe the number and type of root, and find the exact solution using the quadratic formula given #4x^2+7=9x#?

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Answer 1 · 2016-11-21T16:34:50

#Delta=-31<0" "# so roots are complex.

#x=9/8+-isqrt31/8#

1) rearrange to the form #""ax^2+bx+c=0#

#4x^2+7=9x#

#4x^2-9x+7=0#

2) check the discriminant#" "Delta=b^2-4ac#

#Delta=(-9)^2-4xx4xx7#

#Delta=81-112=-31#

types of roots

#Delta>0" "#real distinct roots

#Delta=0" "#real and equal roots

#Delta<0" "#roots are complex.

In this case #" "Delta=-31<0" "# so roots are complex.

3) so the exact solutions

using the formula

#x=(-b+-sqrtDelta)/(2a)#

#x=(-(-9)+-sqrt(-31))/(2xx4)#

#x=(9+-isqrt31)/8#

#x=9/8+-isqrt31/8#