How do you find the value of the discriminant and determine the nature of the roots #8b^2-6b+3=5b^2#?

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Answer 1 · 2017-06-11T19:12:34

Real and equal.

We have: #8 b^(2) - 6 b + 3 = 5 b^(2)#

#Rightarrow 3 b^(2) - 6 b + 3 = 0#

The formula for finding the discriminant #Delta# of a quadratic function is #Delta = b^(2) - 4 a c#:

#Rightarrow Delta = (- 6)^(2) - 4 (3) (3)#

#Rightarrow Delta = 36 - 36#

#therefore Delta = 0#

Now, according to Siyavula, "if #Delta = 0#, the roots are equal and we can say that there is only one root".

Therefore, the roots of #8 b^(2) - 6 b + 3 = 5 b^(2)# are real and equal.