A student tries to factor the expression 6x2 3x 7 6x2 3x

A student tries to factor the expression 6x^2 - 3x + 7: 6x^2 - 3x + 7 = 3x(2x - 1) + 7 Did the student factor the expression correctly? Explain.

Solution

solution

6x^2-3x+7=0

student is wrong.

we cant factor it.

Solving    6x²+3x+7 = 0 by the Quadratic Formula .

According to the Quadratic Formula,  x  , the solution for   Ax²+Bx+C  = 0  , where  A, B and  C  are numbers, often called coefficients, is given by :
                           x=-b+- sqrt(b^2-4ac)/2a

In our case,  A   =     6
                      B   =    3
                      C   =   7

Accordingly,  B²  -  4AC   =
                     9 - 168 =
                     -159

Applying the quadratic formula :

x  =  ( -3 ± 12.610 i ) / 12