If it has no real solutions, that means the graph does not intersect the x axis
since we have ax^2+bx+c=0, the parabola opens either up or down
since the vertex is in the second quadrant (x is negative and y is positive in this reigon) and the graph does not cross the x axis, the parabola must open up
if the value of 'a' is positive, then the parabola opens up
so 'a' must be positive
if it is translated to the 4th quadrant, then the vertex is now below the x axis
it will now have 2 x intercepts because the vertex is in the 4th quadrant and look at a graph of a parabola opening up with vertex in 4th quadrant and seehow many time it crosses the x axis
Answer:
x=10 x=-2
Step-by-step explanation:
(x − 3)(x − 5) = 35
FOIL
x^2 -5x-3x+15 = 35
Combine like terms
x^2 -8x+15 = 35
Subtract 35 from each side
x^2 -8x+15-35 = 35-35
x^2 -8x-20 =0
Factor
What 2 numbers multiply to -20 and add to -8
-10*2 = -20
-10 +2 = -8
(x-10)(x+2) =0
Using the zero product property
x-10 =0 x+2 = 0
x=10 x=-2
Answer:
RC = 40
Step-by-step explanation:
Note that the circumcentre is equally distant from the triangle's 3 vertices.
That is : PC = RC = QC
Equate any pair and solve for x
Using RC = PC, then
5x - 15 = 3x + 7 ( subtract 3x from both sides )
2x - 15 = 7 ( add 15 to both sides )
2x = 22 ( divide both sides by 2 )
x = 11
Hence
RC = (5 × 11) - 15 = 55 - 15 = 40 units
Answer:
Cannot be factored further.
Step-by-step explanation:
I'm just gonna pretend that the equal sign isn't there.
First, simplify the numbers. when you simplify, you should get 7x^2-64.
This is the final. Your answer should be it cannot be factored further.
