Answer:
If Discriminant,
Then it has Two Real Solutions.
Step-by-step explanation:
To Find:
If discriminant (b^2 -4ac>0) how many real solutions
Solution:
Consider a Quadratic Equation in General Form as

then,
is called as Discriminant.
So,
If Discriminant,
Then it has Two Real Solutions.
If Discriminant,
Then it has Two Imaginary Solutions.
If Discriminant,
Then it has Two Equal and Real Solutions.
Answer:
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Step-by-step explanation:
Answer:
21
Step-by-step explanation:
3x3x3=27
27-6=21
The longest possible altitude of the third altitude (if it is a positive integer) is 83.
According to statement
Let h is the length of third altitude
Let a, b, and c be the sides corresponding to the altitudes of length 12, 14, and h.
From Area of triangle
A = 1/2*B*H
Substitute the values in it
A = 1/2*a*12
a = 2A / 12 -(1)
Then
A = 1/2*b*14
b = 2A / 14 -(2)
Then
A = 1/2*c*h
c = 2A / h -(3)
Now, we will use the triangle inequalities:
2A/12 < 2A/14 + 2A/h
Solve it and get
h<84
2A/14 < 2A/12 + 2A/h
Solve it and get
h > -84
2A/h < 2A/12 + 2A/14
Solve it and get
h > 6.46
From all the three inequalities we get:
6.46<h<84
So, the longest possible altitude of the third altitude (if it is a positive integer) is 83.
Learn more about TRIANGLE here brainly.com/question/2217700
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