True or False?
If a, b, and c denote real numbers and p(x)=ax^2+bx+c, x € ℝ, then there exists a real number x0 such that p(x0)=0.
Please show work
then there exist two different solutions
there is no solutions
there are two same solutions
for more information see link below
Quadratic function - Wikipedia, the free encyclopedia
Putting this equation in standard form we have
Assume that , we can conclud that this is graph of a parabola that opens upwards and has vetex . Again, since the parabola opens upward,
And since there are enumerable instances where this statement does not hold, the answer is false
But the question isn't asking if this holds for all cases. The statement is an existential statement; one that asks us to find at least one case where the statement is true.And since there are enumerable instances where this statement does not hold, the answer is false
This is a true statement under certain cases. Again, it all depends on the value of the discriminant . IfTrue or False?
If and , , then there exists a real number such that .
, then there are two solutions (so there exists more than one ).
, there there is only one solution (thus exists).
, there there is no real solution. This implies that a does not exist.
To summarize, the only time when an exists is when . Also, the value of is the real zero(s) of the quadratic equation.
Consider . Since , we search for an such that . So in essence, we solve . But or . So in this case, there exists two possible values for : and , where both values for are real numbers.
can you help me with this one:
You were right about the last statement of my argument, a small error, but the result is still sound. I cahnged it. But by reading the question again, and taking note of the phrase "there exists" , I interpret this to mean that "there must exist" or 'there always exists". And you and I both know that this is a false statement.
I will attempt to reword the statement. Note that a,b, and c can be any real numbers.
--For any given parabola, there exists at least one place where it touches the x-axis.--
Is this ridiculous, or is this ridiculous?
"Exists is not a predicate."Immanuel Kant.