Question

Find the discriminant of the equation 3x² - 2x - 8= 0 and hence find the nature of the roots. Find them if they're real.​

Answer 1

Step-by-step explanation:

3x^2-2x-8=0

D=b^2-4ac

D= (-2)^2-4(3)(8)

D=4-96

D=-92

as,D<0

therefore the roots are not real.

Answer 2

The roots are real and unequal and x = 2 or, - 0.75

Step-by-step explanation:

The given quadratic equation :

3$x^2$ - 2x - 8 = 0

Here, a = 3, b = - 2 and c = - 8

To find, the discriminant(D) = ? and nature of roots = ?

D = $b^2$ - 4ac

= $(-2)^2$ - 4(3)(-8)

= 4 + 96

= 100,

D > 0, the roots are real and unequal.

∴ x = $\dfrac{-b±\sqrt{D}}{2a}$

= $\dfrac{-(-2)±\sqrt{100}}{2(3)}$

= $\dfrac{2±10}{6}$

= $\dfrac{2+10}{6}$ or, $\dfrac{2-10}{6}$

= 2 or, $\dfrac{-4}{3}$

= 2 or, - 0.75

Thus, the roots are real and unequal and x = 2 or, - 0.75