Question

find the quadratic polynomial whose sum of zeros is 3 and product of zeros is 2​

Answer 1

Answer :

x² - 3x + 2

Note:

★ The possible values of the variable for which the polynomial becomes zero are called its zeros .

★ A quadratic polynomial can have atmost two zeros .

★ The general form of a quadratic polynomial is given as ; ax² + bx + c .

★ If α and ß are the zeros of the quadratic polynomial ax² + bx + c , then ;

• Sum of zeros , (α + ß) = -b/a

• Product of zeros , (αß) = c/a

★ If α and ß are the zeros of a quadratic polynomial , then that quadratic polynomial is given as : k•[ x² - (α + ß)x + αß ] , k ≠ 0.

Solution :

Let α and ß be the zeros of the required quadratic polynomial .

Then ,

According to the question , we have ;

• Sum of zeros , (α + ß) = 3

• Product of the zeros , αß = 2

Now ,

The required quadratic polynomial will be given as ; k•[ x² - (α + ß)x + αß ] , k ≠ 0

ie. , k•[ x² - 3x + 2 ] , k ≠ 0

For k = 1 , the Quadratic polynomial will be ;

→ k•[ x² - 3x + 2 ] , k ≠ 0

→ 1•[ x² - 3x + 2 ]

→ x² - 3x + 2

Hence ,

The required quadratic polynomial is ;

x² - 3x + 2