What value(s) of x make each of these undefined?
#1: 25x-x^2
my answer:
x=0 and x=25
#2: 5x^2-3x-2
my answer: x=1
Are these both correct? Isn't there another solution for #2, or is the only one x=1?
both of your expressions are defined for all values of x.
In most cases, undefined values arise when you divide by zero or attempt to take the square root of a negative in the set of real numbers.
are you sure your expressions are not denominators of some other terms?
The first is a denominator; the full term is 6 over 25x-x^2
And the second is also a denominator with the full term being 2x-1 over 5x^2-3x-2
you should have said so in the first place.
That was very important.
for a denominator of 25x - x^2, 0 and 25 are the correct restrictions for x
for the denominator of 5x^2 - 3x - 2
which factors to (x-1)(5x+2)
x cannot be 1 or -2/5
So for the second one would I put "no solution"?
Your answer for #1 is correct. To find the values of x that make the expression 25x - x^2 undefined, you need to find the values of x that make the denominator of the expression equal to zero. In this case, the denominator is -x^2, which means the expression is undefined when x = 0 (because 0 is the only value that makes the denominator equal to zero), and when x = 25 (because plugging 25 into the expression results in a division by zero).
For #2, the expression 5x^2 - 3x - 2 is a quadratic polynomial. To find the values of x that make it undefined, we need to check if the expression has any factors or if the quadratic equation has any real roots. In this case, the expression can be factored as (x - 2)(5x + 1), which means it is equal to zero when x = 2 or x = -1/5.
So, for #2, the values of x that make the expression undefined are x = 2 and x = -1/5. Therefore, x = 1 is not the only solution. It is essential to factor the quadratic expression to find all the values of x that make the expression equal to zero.