How do you find the value of the discriminant and determine the nature of the roots #4x² – 8x = 3 #?
1 Answer
Explanation:
Given:
#4x^2-8x=3#
Subtract
#4x^2-8x-3 = 0#
This is in the standard form
It has discriminant
#Delta = b^2-4ac = (-8)^2-4(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 non-real roots. If#-Delta# is a perfect square then the imaginary coefficient is rational.