Question

Please help quick!!

What is the solution set of the following equation? 6x 2 = 13x + 5
{5/3, -1/2}
{-1/3, 5/2}
{-3, 2/5}

Answer 1

C
6x^2-13X-5=0
(3X+1)(2X-5)
3x-1=0
X=1/3. 2x-5=0. X= 5/2

Answer 2

Option A is correct.

`\{(5)/(3), -(1)/(3)\}`

Explanation:

Given the equation:
`6x^2=13x+5`

we can write this as:

`6x^2-13x-5=0`

A quadratic equation is of the form:
`ax^2+bx+c=0`

then the solution is given by:

`x = (-b\pm√(b^2-4ac))/(2a)`

On comparing with the given equation we have;

a = 6, b = -13 and c = -5 then;

Substitute the given values we have

`x = (-(-13)\pm√((-13)^2-4(6)(-5)))/(2(6))`

`x = (13\pm√(169+120))/(12)`

Simplify:

`x = (13 \pm√(289))/(12)`

`x = (13 \pm 17)/(12)`

Then;

`x = (13+17)/(12)` and
`x = (13-17)/(12)`

⇒
`x = (20)/(12)` and
`x = -(4)/(12)`

⇒
`x = (5)/(3)` and
`x = -(1)/(3)`

Therefore, the solution for the given equation are:

`\{(5)/(3), -(1)/(3)\}`