# Use the discriminant to predict the nature of the roots, then use the quadratic formula to find the roots. 9x^2 + 3x - 8 = 0

baxthum8 | High School Teacher | (Level 3) Associate Educator

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The discriminant of the equation `9x^2 + 3x - 8=0`

would be defined by `b^2 - 4ac`

Therefore:  b = 3,  a = 9, and c = -8

So, the discriminant is `3^2 - 4(9)(-8)`

`9 + 288 = 297`

Since discriminant is `>=0`  then we will have real roots.

`(-3+-sqrt(297))/(2(9))`

`(-3+-sqrt(297))/18` Simplify `sqrt(297)`

`sqrt(297) =sqrt(9)*sqrt(33)` = `3sqrt(33)`

So thiswil give us:  `(-3+-3sqrt(33))/18`

Since everything has factor of 3, we can cancel to give us:

`(-1+-sqrt(33))/6`

so the roots are:  `x = (-1+-sqrt(33))/6`

` `

atyourservice | Student, Grade 11 | (Level 3) Valedictorian

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`9x^2 + 3x - 8 = 0`

`a=9` `b=3 ` `c=-8 `           `b^2-4ac`

`3^2-4(9)(-8)`

`9+288=297 `  297 is the discriminant since it is bigger than 0 it has 2 real solutions. To find the roots use:

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

`(-3+-sqrt(297))/(2(9))`

`(-3+-sqrt(297))/(18)`

`(-3-sqrt(297))/(18) `     `x=-1.12`

`(-3+sqrt(297))/(18) `     `x=0.79`