Question

find the quadratic polynomial having sum of their roots and products of their roots are given as(0,-5)​

Answer 1

Answer :

x² - 5

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 .

Also ,

It is given that , the sum and the product of the zeros of the required quadratic polynomial are given as (0 , -5) .

Thus ,

α + ß = 0

αß = -5

Also ,

We know that , 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.

Thus ,

The required quadratic polynomial will be ;

=> k•[ x² - 0•x + (-5) ] , k ≠ 0 .

=> k•[ x² - 5 ] , k ≠ 0

If k = 1 , then the quadratic polynomial will be ; x² - 5 .

Answer 2

According to the question

sum of zeroes = 0

and

product of zeroes = -5

standard form x²-(a+b)x+ab =0

x² -0x + -5 =0

x²-5=0