Answer:
-25 is the integer
Step-by-step explanation:
Answer:
No.
Step-by-step explanation:
This is because 5:2 could mean there are 5 circles to 2 triangles and 2:5 could mean 2 circles to 5 triangles.
5 circles is not the same as 2 circles as 2 triangles is not the same as 5 triangles.
The quadratic equations that have real roots are
and
.
<h3>What is the discriminant of a quadratic equation?</h3>
The value of a discriminant of a quadratic equation shows how many roots f(x) have. If the value of the discriminant is greater than 0 then the quadratic equation has real and distinct roots and if the value of the discriminant is equal to 0, then the quadratic equation has real and same roots. In case the value of the discriminant is less than zero then the quadratic equation will have no real roots.
In order to know if the quadratic equation has real roots or not, we need to find the discriminant of the given quadratic equations,
A.) ![-x^2+2x -6 = 0](https://tex.z-dn.net/?f=-x%5E2%2B2x%20-6%20%3D%200)
Here, a= -1, b=2 and c=-6
![D = b^2 -4ac](https://tex.z-dn.net/?f=D%20%3D%20b%5E2%20-4ac)
![D = 4 -24\\D = -20](https://tex.z-dn.net/?f=D%20%3D%204%20-24%5C%5CD%20%3D%20-20)
As the value of the discriminant is negative it will not have real roots.
B.) ![-2x^2+3x+4 = 0](https://tex.z-dn.net/?f=-2x%5E2%2B3x%2B4%20%3D%200)
Here, a= -2, b=3 and c=4
![D = b^2 -4ac](https://tex.z-dn.net/?f=D%20%3D%20b%5E2%20-4ac)
![D = 9 +32\\D = 41](https://tex.z-dn.net/?f=D%20%3D%209%20%2B32%5C%5CD%20%3D%2041)
As the value of the discriminant is positive it will have real roots.
C.) ![2x^2+x-6 = 0](https://tex.z-dn.net/?f=2x%5E2%2Bx-6%20%3D%200)
Here, a=2, b=1 and c=-6
![D = b^2 -4ac](https://tex.z-dn.net/?f=D%20%3D%20b%5E2%20-4ac)
![D = 1 +48\\D =49](https://tex.z-dn.net/?f=D%20%3D%201%20%2B48%5C%5CD%20%3D49)
As the value of the discriminant is positive it will have real roots.
A.) ![2x^2 -x+3 = 0](https://tex.z-dn.net/?f=2x%5E2%20-x%2B3%20%3D%200)
Here, a=2, b=-1 and c=3
![D = b^2 -4ac](https://tex.z-dn.net/?f=D%20%3D%20b%5E2%20-4ac)
![D = 1-24\\D = -23](https://tex.z-dn.net/?f=D%20%3D%201-24%5C%5CD%20%3D%20-23)
As the value of the discriminant is negative it will not have real roots.
Learn more about Discriminant:
brainly.com/question/15884086
The required line is parallel to line x + y = 1 and passes through point (1, 1).
For parallel lines, slope is equal.
x + y = 1
y = -x + 1 => slope is -1
Line passing though point (1, 1) with slope = -1 is given by y - 1 = -(x - 1)
y - 1 = -x + 1
y + x = 1 + 1 = 2
i.e. Equation of the required lin is x + y = 2
Required distance is the distance between point (1, 1) and the point of intersection of lines x + y = 2 and 2x - 3y = 4.
x + y = 2 . . . (1)
2x - 3y = 4 . . . (2)
(1) x 2 => 2x + 2y = 4 . . . (3)
(2) - (3) => -5y = 0 => y = 0
From (1), x + 0 = 2 => x = 2.
i.e. the point of intersection of lines x + y = 2 and 2x - 3y = 4 is (2, 0).
Required distance is