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

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

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

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

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

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=9x4x^2+7=9x?