Question

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

Answer 1

x1= 2/3, x2 = -4

Explanation:

3x² + 10x + c = 0

Formula for the roots of the quadratic equation is

`x = (-b +/-√(b^2-4ac) )/(2a)`

Where a = 3, b=10, c=c for our equation 3x² + 10x + c = 0.

`x=\frac{-10+/-\sqrt{10^(2)-4*3c} }{2*3} \\\\x=(-10+/-√(100-12c) )/(6) \\\\x_(1) =(-10+√(100-12c) )/(6) \\\\x_(2) =(-10-√(100-12c) )/(6) \\\\x_(1)-x{_2}=(-10+√(100-12c) )/(6) -((-10-√(100-12c) )/(6) )\\\\x_(1)-x{_2}= (2√(100-12c) )/(6) =(√(100-12c) )/(3) \\\\x_(1)-x{_2}=(√(100-12c) )/(3) = 4(2)/(3) =(14)/(3) \\\\√(100-12c) =14\\(√(100-12c) )^(2)=14^(2)100-12c = 196\\12c=100-196\\c=-8`

`x=(-10+/-√(100-12(-8)) )/(6) = (-10+/-√(196) )/(6) =(-10+/-14)/(6) \\\\x_(1) =(4)/(6) =(2)/(3) \\x_(2) =(-24)/(6) =-4`