Question

Q11. Find a quadratic polynomial ,the sum and product of whose zeros are √2 and -3/2 respectively.
​

Answer 1

Answer :

½ • (2x² - 2√2x - 3)

OR 2x² - 2√2x - 3

Solution :

★ Given :

Sum of zeros = √2

Product of zeros = -3/2

★ To find : Quadratic polynomial

Note :

If a and b are the zeros of a quadratic polynomial then it is given as ;

k•[x² - (a+b)x + ab] , k ≠ 0 .

Here ,

Sum of zeros = √2

=> a + b = √2

Also ,

Product of zeros = -3/2

=> ab = -3/2

Thus ,

The required quadratic polynomial will be given as ; k•[x² - (a+b)x + ab]

=> k•[x² - √2x + (-3/2)]

=> k•(x² - √2x - 3/2)

=> k•½ • (2x² - 2√2x - 3)

For k = 2 , the quadratic polynomial will be ;

2x² - 2√2x - 3 .

Hence ,

The required quadratic polynomial is ;

½ • (2x² - 2√2x - 3)

OR 2x² - 2√2x - 3