How many real number solutions does the equation have
y=-4x^2+7x-8
none
one
two
infinite
How many real number solutions does the equation have
y=3x^2+18x+27
none
one
two
infinite
Thank you!
4 answers
is number 1 none?
Mrs sue can you help me with question 2?
You state the equation as a function, so to speak of real number solutions makes no sense.
There are an infinite number of solutions, any ordered pair satisfying the equation would be one.
You probably want the solution to
-4x^2 + 7x - 8 = 0
in both cases, it depends on the value of the discriminant b^2 - 4ac
for the first:
b^2 - 4ac
= 49-4(-4)(-8) = negative
So -4x^2 + 7x - 8 = 0 has no real solution
here is your graph, notice that the curve does not reach the x-axis
http://www.wolframalpha.com/input/?i=plot+y%3D-4x%5E2%2B7x-8+
for 3x^2 + 18x + 27 = 0
b^2- 4ac
= 18^2 - 4(3)(27) = 0
so there is ONE real solution
verification:
http://www.wolframalpha.com/input/?i=plot+y%3D3x%5E2%2B18x%2B27
graph touches the x-axis once, so one solution.
You should make yourself familiar to the properties of solutions of a quadratic based on the sign of b^2 - 4ac
This should be found in your text or your notes.
There are an infinite number of solutions, any ordered pair satisfying the equation would be one.
You probably want the solution to
-4x^2 + 7x - 8 = 0
in both cases, it depends on the value of the discriminant b^2 - 4ac
for the first:
b^2 - 4ac
= 49-4(-4)(-8) = negative
So -4x^2 + 7x - 8 = 0 has no real solution
here is your graph, notice that the curve does not reach the x-axis
http://www.wolframalpha.com/input/?i=plot+y%3D-4x%5E2%2B7x-8+
for 3x^2 + 18x + 27 = 0
b^2- 4ac
= 18^2 - 4(3)(27) = 0
so there is ONE real solution
verification:
http://www.wolframalpha.com/input/?i=plot+y%3D3x%5E2%2B18x%2B27
graph touches the x-axis once, so one solution.
You should make yourself familiar to the properties of solutions of a quadratic based on the sign of b^2 - 4ac
This should be found in your text or your notes.
bru why dont mfs just add the whole test💀
4 answers