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2 answers:
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Answer:
Problem 23)
Problem 24)
Step-by-step explanation:
step 1
Find the slope of the given line
The formula to calculate the slope between two points is equal to
we have
Substitute the values
step 2
Problem 23
we know that
If two lines are perpendicular then the product of its slopes is equal to minus 1
so
Find the slope of the line
we have
substitute in the equation and solve for m2
with the slope m2 and the point find the equation of the line
Remember that
The equation of the line in slope intercept form is equal to
we have
-----> the given point is the y-intercept
substitute
step 3
Problem 24
we know that
If two lines are parallel, then its slopes are the same
so
with the slope m1 and the point find the equation of the line
The equation of the line in slope intercept form is equal to
we have
-----> the given point is the y-intercept
substitute
The general form of a quadratic (second degree) equation is
, where
is called the Discriminant.
The Discriminant determines how many roots the equation will have as follows:
i) if D>0, the equation has 2 roots.
ii) if D=0, the equation has 1 double root.
iii) if D<0, the equation has no roots.
In our equation,
, a=1, b=-5, c=7
so the discriminant is D=(-5)^2-4*1*7=25-28<0
Thus the equation has no roots.
Remark: the equation has no roots in the Real numbers, but it has 2 roots in a larger set of numbers to be discussed in the future, the Complex numbers.
The Discriminant determines how many roots the equation will have as follows:
i) if D>0, the equation has 2 roots.
ii) if D=0, the equation has 1 double root.
iii) if D<0, the equation has no roots.
In our equation,
so the discriminant is D=(-5)^2-4*1*7=25-28<0
Thus the equation has no roots.
Remark: the equation has no roots in the Real numbers, but it has 2 roots in a larger set of numbers to be discussed in the future, the Complex numbers.