Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes

1 answer:

4 0

The quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively as 3 /2 and 5 is 2x² - 3x + 10

<h3>What is a quadratic polynomial?</h3>

A quadratic polynomial is a polynomial of the form ax² + bx + c

<h3>How to find the quadratic polynomial?</h3>

For any given quadratic polynomial we have

x² - (sum of zeros)x + (products of zeros) = 0

Given that the sum and product of its zeroes respectively 3/2 and 5,

We have that

sum of zeroes = 3/2 and
product of zeros = 5

Substituting the values of the variables into the equation, we have

x² - (sum of zeros)x + (products of zeros) = 0

x² - (3/2)x + (5) = 0

Multiplying through by 2, we have

2 × x² - 2 × (3/2)x + 2 × (5) = 0 × 2

2x² - 3x + 10 = 0

So, the quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively as 3/2 and 5 is 2x² - 3x + 10

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