# Use the discriminant to predict the nature of the roots, then use the quadratic formula to find the roots. 8x^2 - 4x - 3 = 0

baxthum8 | Certified Educator

The discriminant of a quadratic is defined by:  `b^2 - 4ac.`

In the quadratic equation `8x^2 - 4x - 3 = 0`  , a = 8, b = -4, and c = -3.

So discriminant is `(-4)^2 - 4(8)(-3) = 112`

Discriminant is greater than or qual to 0, therefore we have real roots.

To solve use the quadratic formula:

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

So we have:  `(4+-sqrt(112))/16`

We must simplify the radical:  `sqrt(112) =sqrt(16)*sqrt(7)= 4sqrt(7)`

So now we have:  `(4+-4sqrt(7))/16 = (1+-sqrt(7))/4`

So the real roots are:  `x = (1+-sqrt(7))4`

baxthum8 | Certified Educator

Mistake on last line:  `x = (1+-sqrt(7))/4`

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atyourservice | Student

`8x^2 - 4x - 3 = 0`   use the formula `b^2-4ac`

`a=8` `b=-4` `c=-3`

`-4^2-4(8)(-3) `   simplify it

`16+96= 112` the discriminant is 112, meaning there are 2 real solutions

`(4+-sqrt(112))/(2(8))`

`(4+-sqrt(112))/(16)`

the solutions are

`(4+sqrt(122))/(16)`

and

`(4-sqrt(122))/(16)`