Question

Write the quadratic polynomial , the sum and product of whose zeroes are 3 and -2 respectively

Answer 1

We know that any quadratic equation will be of the form :

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

Given:

$\alpha + \beta = 3 \\ \alpha \beta = - 2$

So the quadratic polynomial is:

$k( {x}^{2} - ( 3)x +( - 2)) = 0 \\ k( {x}^{2} - 3x - 2 =) 0 \\ {x}^{2} - 3x - 2 = 0$

Answer 2

Answer:

x^2 - 3x - 2

Step-by-step explanation:

Let the zeroes be α and β

According to the question:

α +  β = 3             αβ =(-2)

The quadratic polynomial whose sum and product of the zeroes are given is given by :

= x^2 - ( α +  β ) x + αβ

Then the quadratic polynomial will be :

= x^2 - 3x + (-2)

= x^2 - 3x - 2

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