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Answer:
<em>18</em> values for n are possible.
Step-by-step explanation:
Given the quadratic polynomial:
such that:
Roots are positive prime integers and
To find:
How many possible values of are there ?
Solution:
First of all, let us have a look at the sum and product of a quadratic equation.
If the quadratic equation is:
and the roots are: and
Then sum of roots,
Product of roots,
Comparing the given equation with standard equation, we get:
A = 1, B = -m and C = n
Sum of roots,
Product of roots,
We are given that
and
are positive prime integers such that their sum is less than 20.
Let us have a look at some of the positive prime integers:
2, 3, 5, 7, 11, 13, 17, 23, 29, .....
Now, we have to choose two such prime integers from above list such that their sum is less than 20 and the roots can be repetitive as well.
So, possible combinations and possible value of are:
So,as shown above <em>18 values for n are possible.</em>
Answer:
A
Step-by-step explanation:
Calculate the slope of the given points with the point (- 2, 5 )
If the slope is - then the point is on the line
Calculate slope m using the slope formula
m =
with (x₁, y₁ ) = (- 2, 5) and (x₂, y₂ ) = (6, - 1)
m = =
= -
← point (6, - 1) is on the line
Repeat with (x₁, y₁ ) = (- 2, 5 ) and (x₂, y₂ ) = (2, 8)
m = =
← point (2, 8) is not on the line
Repeat with (x₁, y₁ ) = (- 2, 5) and (x₂, y₂ ) = (- 5, 1)
m = =
=
← point (- 5, 1) is not on the line
Repeat with (x₁, y₁ ) = (- 2, 5) and (x₂, y₂ ) = (1, 1)
m = = -
← point (1, 1) is not on the line
Thus the point on the line is (6, - 1 ) → A