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Answer:
product will 127xsquare
sum will 99x
prime factors of 127-
so xsquare +99x+11square+6
so now product will 11
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wo solutions were found :
x =(-99-√9293)/2=-97.700
x =(-99+√9293)/2=-1.300
Reformatting the input :
Changes made to your input should not affect the solution:
(1): "x2" was replaced by "x^2".
Step by step solution :
Step 1 :
Trying to factor by splitting the middle term
1.1 Factoring x2+99x+127
The first term is, x2 its coefficient is 1 .
The middle term is, +99x its coefficient is 99 .
The last term, "the constant", is +127
Step-1 : Multiply the coefficient of the first term by the constant 1 • 127 = 127
Step-2 : Find two factors of 127 whose sum equals the coefficient of the middle term, which is 99 .
-127 + -1 = -128
-1 + -127 = -128
1 + 127 = 128
127 + 1 = 128
Observation : No two such factors can be found !!
Conclusion : Trinomial can not be factored
Equation at the end of step 1 :
x2 + 99x + 127 = 0
Step 2 :
Parabola, Finding the Vertex :
2.1 Find the Vertex of y = x2+99x+127
Parabolas have a highest or a lowest point called the Vertex . Our parabola opens up and accordingly has a lowest point (AKA absolute minimum) . We know this even before plotting "y" because the coefficient of the first term, 1 , is positive (greater than zero).
Each parabola has a vertical line of symmetry that passes through its vertex. Because of this symmetry, the line of symmetry would, for example, pass through the midpoint of the two x -intercepts (roots or solutions) of the parabola. That is, if the parabola has indeed two real solutions.
Parabolas can model many real life situations, such as the height above ground, of an object thrown upward, after some period of time. The vertex of the parabola can provide us with information, such as the maximum height that object, thrown upwards, can reach. For this reason we want to be able to find the coordinates of the vertex.
For any parabola,Ax2+Bx+C,the x -coordinate of the vertex is given by -B/(2A) . In our case the x coordinate is -49.5000
Plugging into the parabola formula -49.5000 for x we can calculate the y -coordinate :
y = 1.0 * -49.50 * -49.50 + 99.0 * -49.50 + 127.0
or y = -2323.250
x =(-99-√9293)/2=-97.700
x =(-99+√9293)/2=-1.300
Reformatting the input :
Changes made to your input should not affect the solution:
(1): "x2" was replaced by "x^2".
Step by step solution :
Step 1 :
Trying to factor by splitting the middle term
1.1 Factoring x2+99x+127
The first term is, x2 its coefficient is 1 .
The middle term is, +99x its coefficient is 99 .
The last term, "the constant", is +127
Step-1 : Multiply the coefficient of the first term by the constant 1 • 127 = 127
Step-2 : Find two factors of 127 whose sum equals the coefficient of the middle term, which is 99 .
-127 + -1 = -128
-1 + -127 = -128
1 + 127 = 128
127 + 1 = 128
Observation : No two such factors can be found !!
Conclusion : Trinomial can not be factored
Equation at the end of step 1 :
x2 + 99x + 127 = 0
Step 2 :
Parabola, Finding the Vertex :
2.1 Find the Vertex of y = x2+99x+127
Parabolas have a highest or a lowest point called the Vertex . Our parabola opens up and accordingly has a lowest point (AKA absolute minimum) . We know this even before plotting "y" because the coefficient of the first term, 1 , is positive (greater than zero).
Each parabola has a vertical line of symmetry that passes through its vertex. Because of this symmetry, the line of symmetry would, for example, pass through the midpoint of the two x -intercepts (roots or solutions) of the parabola. That is, if the parabola has indeed two real solutions.
Parabolas can model many real life situations, such as the height above ground, of an object thrown upward, after some period of time. The vertex of the parabola can provide us with information, such as the maximum height that object, thrown upwards, can reach. For this reason we want to be able to find the coordinates of the vertex.
For any parabola,Ax2+Bx+C,the x -coordinate of the vertex is given by -B/(2A) . In our case the x coordinate is -49.5000
Plugging into the parabola formula -49.5000 for x we can calculate the y -coordinate :
y = 1.0 * -49.50 * -49.50 + 99.0 * -49.50 + 127.0
or y = -2323.250
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