if 1/5 and -2 are respectively product and sum of the zeroes of a quadratic polynomial. Find the polynomial.
2 answers:
Answer:
this might be the equation
Step-by-step explanation:
To find: Quadratic Polynomial.
where , ( α + β ) is sum of zeroes and αβ is product of zeroes.
Answer:
Below
Step-by-step explanation:
The polynomial has the following form:
● ax^2 + bx + c
Let x'and x" be the zeroes
● x x'= (1/5)
● x + x' = -2
When we khow the sum and the product of two numbers we can find them by solving the following quadratic equation:
● x^2 - Sx + p
S is the sum of those numbers and P is their product
● x^2 - (-2x) + 1/5
● x^2 + 2x + (1/5)
We will solve this equation by graphing it. The solutions are the intersection points with the x-axis
The solutions are approximatively -0.1 and - 1.9 ( pictures below)
● x'= -0.1
● x"= -1.9
The intial polynomial can be written in the factored form using the zeroes as:
● a ( x - x') (x- x")
● a (x -(-0.1)) ( x -(-1.9))
● a ( x+0.1) ( x+1.9)
The sum of the zeroes is -2 and their product is (1/5)
Assuming a = 1
● (x + 0.1) ( x +1.9)
● x^2 + 1.9x + 0.1x + 0.19
● x^2 + 2x + 0.19
Multiply by 100 to eliminate the decimal numbers
● 100x^2 + 200x + 19
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Three important properties of the diagonals of a rhombus that we need for this problem are:
1. the diagonals of a rhombus bisect each other
2. the diagonals form two perpendicular lines
3. the diagonals bisect the angles of the rhombus
First, we can let O be the point where the two diagonals intersect (as shown in the attached image). Using the properties listed above, we can conclude that ∠AOB is equal to 90° and ∠BAO = 60/2 = 30°.
Since a triangle's interior angles have a sum of 180°, then we have ∠ABO = 180 - 90 - 30 = 60°. This shows that the ΔAOB is a 30-60-90 triangle.
For a 30-60-90 triangle, the ratio of the sides facing the corresponding anges is 1:√3:2. So, since we know that AB = 10, we can compute for the rest of the sides.
Similarly, we have
Now, to find the lengths of the diagonals,
So, the lengths of the diagonals are 10 and 10√3.
Answer: 10 and 10√3 units
1. the diagonals of a rhombus bisect each other
2. the diagonals form two perpendicular lines
3. the diagonals bisect the angles of the rhombus
First, we can let O be the point where the two diagonals intersect (as shown in the attached image). Using the properties listed above, we can conclude that ∠AOB is equal to 90° and ∠BAO = 60/2 = 30°.
Since a triangle's interior angles have a sum of 180°, then we have ∠ABO = 180 - 90 - 30 = 60°. This shows that the ΔAOB is a 30-60-90 triangle.
For a 30-60-90 triangle, the ratio of the sides facing the corresponding anges is 1:√3:2. So, since we know that AB = 10, we can compute for the rest of the sides.
Similarly, we have
Now, to find the lengths of the diagonals,
So, the lengths of the diagonals are 10 and 10√3.
Answer: 10 and 10√3 units