Question 838938: one of the roots of 3x^2+p=5x, is 2.determine the value of p and the other root
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! if one of the roots of the equation is x = 2, then f(2) must be equal to 0.
start with 3x^2 + p = 5x
subtract 5x from both sides of this equation to get:
3x^2 - 5x + p = 0
replace x with 2 in the equation to get:
3(2)^2 - 5(2) + p = 0
simplify this to get:
12 - 10 + p = 0
simplify further to get:
2 + p = 0
solve for p to get:
p = -2
your expression becomes:
3x^2 - 5x - 2 = 0
factor this equation to get:
(3x + 1) * (x-2) = 0
your factors will be:
x = 2
x = -1/3
to confirm, replace x with -1/3 in the original equation to see if it holds true.
original equation is:
3x^2 + p = 5x
replace p with -2 to get:
3x^2 - 2 = 5x
replace x with (-1/3) to get:
3(-1/3)^2 - 2 = 5*(-1/3)
simplify to get:
3 * 1/9 - 2 = -5/3
convert everything to a common denominator of 9 to get:
3/9 - 18/9 = -15/9
simplify to get:
-15/9 = -15/9
this confirms that -1/3 is a root of the equation.
you can do the same with x = 2 to confirm it is also a solution to the equation.
original equation is:
3x^2 + p = 5x
replace p with -2 to get:
3x^2 - 2 = 5x
replace x with 2 to get:
3(2)^2 - 2 = 5*(2)
simplify to get:
12 - 2 = 10
simplify further to get:
10 = 10
this confirms that 2 is a root of the equation.
|
|
|
