Question

Find the nature of the roots of 6x2 - 8x - 8 = 0.

Answer 1

From the problem, we have :

$6x^2-8x-8=0$

The nature of the roots depends on the value of b^2 - 4ac.

If the result is greater than or equal to 0, the roots are rational.

If the result is less than 0, the roots are irrational.

From the equation, we have :

a = 6, b = -8 and c = -8

$\begin{gathered} b^2-4ac=(-8)^2-4(6)(-8) \\ \Rightarrow64+192=256 \end{gathered}$

Since the result is greater than 0, the roots are rational.