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.

How do you find the value of the discriminant and determine the nature of the roots 8b^2-6b+3=5b^28b^2-6b+3=5b^2?