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

Jun 11, 2017

Real and equal.

#### Explanation:

We have: $8 {b}^{2} - 6 b + 3 = 5 {b}^{2}$

$R i g h t a r r o w 3 {b}^{2} - 6 b + 3 = 0$

The formula for finding the discriminant $\Delta$ of a quadratic function is $\Delta = {b}^{2} - 4 a c$:

$R i g h t a r r o w \Delta = {\left(- 6\right)}^{2} - 4 \left(3\right) \left(3\right)$

$R i g h t a r r o w \Delta = 36 - 36$

$\therefore \Delta = 0$

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.