Question

find the discriminant of the quadratic equation 3 x square minus 6 x minus 4 is equal to zero and natural and its roots​

Answer 1

Answer:

the discriminant is 84..

Answer 2

Given:

The given equation is

$3 {x}^{2} - 6x - 4$

To find:

It's discriminant and roots.

Solution:

The given equation is

$3 {x}^{2} - 6x - 4$

The discriminant d is given as follows-

$d = {b}^{2} - 4ac$

Here a=3,b=-6 and c is equal to -4.

Thus we can write-

$d = { - 6}^{2} - 4 \times 3 \times ( - 4) \\ d = 36 + 48 \\ d = 84$

The value of the discriminant is 84.

As d >0 so, the roots are real.

Again the roots of the equation are given as-

$x = \frac{ - b + \sqrt{d} }{2a} \\ x = \frac{ - b - \sqrt{d} }{2a} \\ x = \frac{ - ( - 6) + \sqrt{84} }{2 \times 3} \\ x = \frac{ + 6 + \sqrt{84} }{6} \\ x = \frac{ - ( - 6) - \sqrt{84} }{2 \times 3} \\ x = \frac{ + 6 - \sqrt{84} }{6}$

Thus, the roots are

$x = \frac{ + 6 + \sqrt{84} }{6} \\x = \frac{ + 6 - \sqrt{84} }{6}$

#SPJ3