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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