Question

Find the quadratic polynomial having roots 1 and -2
​

Answer 1

Answer:

first yor find sum of zeroes

and then,

sum of products

and then solving that we find a quadratic equation

Answer 2

The quadratic polynomial having roots 1 and - 2 is x² + x - 2

Given : The roots of the quadratic polynomial are 1 and - 2

To find : The quadratic polynomial

Tip :

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 4 :

Write down the roots

The roots of the quadratic polynomial are 1 and - 2

Step 2 of 4 :

Find the sum of the roots

The sum of the roots

= 1 + ( - 2 )

= 1 - 2

= - 1

Step 3 of 4 :

Find product of roots

The product of the roots

= 1 × ( - 2 )

= - 2

Step 4 of 4 :

Find the quadratic polynomial

The required Quadratic polynomial is

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

$\sf = {x}^{2} - ( - 1)x + ( - 2)$

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

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