What will be the solution of this? #3x^2-6x+8=0#

2 Answers
Jan 21, 2018

See a solution process below"

Explanation:

We can use the quadratic equation to solve this problem:

The quadratic formula states:

For #color(red)(a)x^2 + color(blue)(b)x + color(green)(c) = 0#, the values of #x# which are the solutions to the equation are given by:

#x = (-color(blue)(b) +- sqrt(color(blue)(b)^2 - (4color(red)(a)color(green)(c))))/(2 * color(red)(a))#

Substituting:

#color(red)(3)# for #color(red)(a)#

#color(blue)(-6)# for #color(blue)(b)#

#color(green)(8)# for #color(green)(c)# gives:

#x = (-color(blue)(-6) +- sqrt(color(blue)(-6)^2 - (4 * color(red)(3) * color(green)(8))))/(2 * color(red)(3))#

#x = (6 +- sqrt(36 - 96))/6#

#x = 6/6 +- sqrt(-60)/6#

#x = 1 +- sqrt(4 * -15)/6#

#x = 1 +- (sqrt(4)sqrt(-15))/6#

#x = 1 +- (2sqrt(-15))/6#

#x = 1 +- sqrt(-15)/3#

Jan 21, 2018

#x=1+-1/3sqrt15i#

Explanation:

#"given a quadratic equation in "color(blue)"standard form"#

#•color(white)(x)ax^2+bx+c=0#

#3x^2-6x+8=0" is in standard form"#

#"with "a=3,b=-6" and "c=8#

#"check the value of the "color(blue)"discriminant"#

#•color(white)(x)Delta=b^2-4ac#

#rArrDelta=(-6)^2-(4xx3xx8)=36-96=-60#

#"since "Delta<0" the equation has no real roots"#

#"but will have 2 "color(blue)"complex conjugate roots"#

#"these can be found using the "color(blue)"quadratic formula"#

#•color(white)(x)x=(-b+-sqrt(Delta))/6#

#rArrx=(6+-sqrt(-60))/6=(6+-2sqrt15i)/6#

#rArrx=6/6+-(2sqrt15i)/6=1+-1/3sqrt15i#