if 1/5 and -2 are respectively product and sum of the zeroes of a quadratic polynomial. Find the polynomial.

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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

b

step-by-step explanation: