Question

Solve for x.....................

Answer 1

C.
`x=(7)/(3)` and
`x=(-3)/(2)`

Explanation:

We have the quadratic equation
`6x^(2)-5x-21=0`.

Now, the roots of the quadratic equation
`ax^(2)+bx+c=0` are given by
`x=\frac{-b\pm \sqrt{b^(2)-4ac}}{2a}`.

So, from the given equation, we have,

a = 6, b = -5, c = -21.

Substituting the values in
`x=\frac{-b\pm \sqrt{b^(2)-4ac}}{2a}`, we get,

`x=\frac{5\pm \sqrt{(-5)^(2)-4* 6* (-21)}}{2* 6}`

i.e.
`x=(5\pm √(25+504))/(12)`

i.e.
`x=(5\pm √(529))/(12)`

i.e.
`x=(5\pm 23)/(12)`

i.e.
`x=(5+23)/(12)` and i.e.
`x=(5-23)/(12)`

i.e.
`x=(28)/(12)` and i.e.
`x=(-18)/(12)`

i.e.
`x=(7)/(3)` and i.e.
`x=(-3)/(2)`

Thus, the value for x are
`(7)/(3)` and
`(-3)/(2)`

Answer 2

Option C is correct, i.e. x = 7/3, x = -3/2.

Explanation:

Given the equation is 6x² -5x + -21 = 0.

Then a = 6, b = -5, c = -21

Using the Quadratic formula, x = ( -b ± √(b² -4ac) )/2a

x = ( +5 ± √((-5)² -4*6*-21) )/2*6

x = ( 5 ± √(25 +504) )/12

x = ( 5 ± √(529) )/12

x = ( 5 ± 23 )/12

x = (5-23)/12 or x = (5+23)/12

x = -18/12 or x = 28/12

x = -3/2 or x = 7/3

Hence, option C is correct, i.e. x = 7/3, x = -3/2.