How do you find the value of the discriminant and determine the nature of the roots #4x² – 8x = 3 #?
1 Answer
Explanation:
Given:
#4x^28x=3#
Subtract
#4x^28x3 = 0#
This is in the standard form
It has discriminant
#Delta = b^24ac = (8)^24(4)(3) = 64+48 = 112#
Since
Note however that
In general, we find:

If
#Delta > 0# is a perfect square, then the quadratic equation has two distinct rational roots. 
If
#Delta > 0# is not a perfect square, then the quadratic equation has two distinct real, but irrational roots. 
If
#Delta = 0# then the quadratic equation has one repeated rational real root. 
If
#Delta < 0# then the quadratic equation has no real roots. It has a complex conjugate pair of nonreal roots. If#Delta# is a perfect square then the imaginary coefficient is rational.