The quadratic equation 3x^2 -19x + 28 = 0 has a solution of x = 4. what is the other solution? * free response question

Hello from MrBillDoesMath!

    7/3

Discussion:

Using standard notation, the solutions of the quadratic ax^2 + bx + c = 0 are given by

x =    ( -b +\-  sqrt * b^2 - 4ac) )  / 2a

In our case a = 3, b = -19, and c = 28

x =   ( -(-19) +\-  sqrt ( (-19)^2 - 4*3*28) ) / ( 2*3)

  =   (  19 +\-  sqrt (361 - 336) ) / 6

  =  ( 19 +\- sqrt(25) ) /6

  = ( 19 +\- 5) / 6

   = (19 + 5) /6 = 24/6 = 4  and  (19-5)/6 = 14/6 = 7/3

The other solution ( not equal to 4) is 7/3

Thank you,

MrB

the answer is:

the answer is:

to solve the problem, we need to remember the quotient of power property, it's defined by the following relation:

if we have a quotienf of powers that have the same base, we need to keep the same base and subtract the exponent of the denominator power to the exponent of the numerator power.

so, we are given the expression:

then, calculating we have:

hence, the answer is:

have a nice day!