The difference between the two roots of the equation 3x^2+10x+c=0 is 4 2/3 . find the solutions for the equation.

Given the equation:

A quadratic equation is in the form: where a, b ,c are the coefficient and a≠0 then the solution is given by :

......[1]

On comparing with given equation we get;

a =3 , b = 10

then, substitute these in equation [1] to solve for c;

Simplify:

Also, it is given that the difference of two roots of the given equation is

i.e,

Here,

,     ......[2]

      .....[3]

then;

simplify:

or

Squaring both sides we get;

Subtract 100 from both sides, we get

Simplify:

-12c = -96

Divide both sides by -12 we get;

c = 8

Substitute the value of c in equation [2] and [3]; to solve

or

or

Simplify:

Now, to solve for ;

or

or

Simplify:

therefore, the solution for the given equation is: and -2.

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