Question

Find the quadratic polynomial whose zeroes are (a+b) and (a-b)?​

Answer 1

Answer:

Sum of zeroes=a+b+a-b

                       =2a

Product of zeroes=(a+b)(a-b)

                             =a²-b²

We know that,

p(x)=x²-(sum of zeroes)x + product of zeroes

     =x²-2ax+a²-b²

Answer 2

The quadratic polynomial whose zeroes are (a + b) and (a - b) is x² - 2ax + (a² - b²)

Given :

The zeroes of a quadratic polynomial are (a + b) and (a - b)

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 zeroes of a quadratic polynomial are (a + b) and (a - b)

Sum of zeroes

= (a + b) + (a - b)

= 2a

Product of the zeroes

= (a + b) × (a - b)

= a² - b²

Step 2 of 2 :

Find the quadratic polynomial

The required quadratic polynomial

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

$\displaystyle \sf{ = {x}^{2} - 2ax + ( {a}^{2} - {b}^{2}) }$

Hence the quadratic polynomial whose zeroes are (a + b) and (a - b) is x² - 2ax + (a² - b²)

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