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
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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