Lenora correctly factored the expression 2x2−11x+15 as (x−3)(2x−5). She then stated that the solutions to the equation 0=2x2−11x+15 are x=3 and x=5.
Did Lenora find the correct solutions to the equation?
no.
x=5 corresponds to a factor of (x-5)
To determine if Lenora found the correct solutions to the equation 0=2x2−11x+15, we need to check if substituting x=3 and x=5 into the equation results in zero.
Let's substitute x=3 into the equation:
0 = 2(3)^2 - 11(3) + 15
0 = 18 - 33 + 15
0 = 0
When we substitute x=3 into the equation, we get zero. So x=3 is a solution to the equation.
Now let's substitute x=5 into the equation:
0 = 2(5)^2 - 11(5) + 15
0 = 50 - 55 + 15
0 = 10
When we substitute x=5 into the equation, we get 10, not zero. So x=5 is not a solution to the equation.
Therefore, Lenora found one correct solution to the equation (x=3), but the other solution (x=5) is incorrect.