Question

A quadratic polynomial with 3 and 2 as the sum and product of its zeros respectively

Answer 1

Step-by-step explanation:

The general quadratic equation is

${x}^{2} - ( \alpha + \beta )x + \alpha \beta = 0$

so the equation is

${x}^{2} - 3x + 2 = 0$

Answer 2

The quadratic polynomial is x² - 3x + 2

Given :

A quadratic polynomial with 3 and 2 as the sum and product of its zeros respectively

To find :

The quadratic polynomial

Concept :

If the Sum of zeroes and Product of the zeroes of a quadratic polynomial is given then the quadratic polynomial is

$\sf{ {x}^{2} -(Sum \: of \: the \: zeroes )x + Product \: of \: the \: zeroes }$

Solution :

Step 1 of 2 :

Write down the Sum of zeroes and Product of the zeroes

By the given

Sum of zeroes = 3

Product of the zeroes = 2

Step 2 of 2 :

Find the quadratic polynomial

Hence the required quadratic polynomial is

$\displaystyle \sf = {x}^{2} -(Sum \: of \: the \: zeroes )x + Product \: of \: the \: zeroes$

$\displaystyle \sf = {x}^{2} -3x + 2$

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