Question

Write a quadratic equation, whose sum and product of zeroes is -5 and 2

respectively.​

Answer 1

Answer:

x² +3x -10

Step-by-step explanation:

general formula of Quadratic polynomial

x²- ( Sum of zeroes)x + products of zeroes

x² - (-5+2)x + (-5 X 2)

x² +3x -10

Answer 2

The required quadratic polynomial sum and product of zeroes is - 5 and 2 respectively is x² + 5x + 2

Given :

The sum and product of zeroes is - 5 and 2 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 :

Find Sum of zeroes and Product of the zeroes

Here it is given that sum and product of zeroes is - 5 and 2 respectively

Sum of zeroes = - 5

Product of the zeroes = 2

Step 2 of 2 :

Find the quadratic polynomial

The required quadratic polynomial

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

$\displaystyle \sf = {x}^{2} -(-5)x + 2$

$\displaystyle \sf{ = {x}^{2} + 5x + 2 }$

Hence the required quadratic polynomial sum and product of zeroes is - 5 and 2 respectively is x² + 5x + 2

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