Question

The quadratic polynomial, the sum of whose zeroes is -5 and their

product is 6, is___________​

Answer 1

Step-by-step explanation:

general form of a quadratic polynomial is..

$x {}^{2} - (sum \: of \: roots)x + (product \: of \: roots)$

therefore the quadratic polynomial is

$x {}^{2} - 5x + 6$

Answer 2

Answer :

x² + 5x + 6

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 :

Here ,

It is given that , the sum of zeros of the required quadratic polynomial is -5 .

Thus ,

α + ß = -5

Also ,

The product of zeros of the required quadratic polynomial is 6 .

Thus ,

αß = 6

Now ,

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 given as ;

=> k•[ x² - (-5)x + 6 ] , k ≠ 0

=> k•[ x² + 5x + 6 ] , k ≠ 0

If k = 1 , then the quadratic polynomial will be x² + 5x + 6 .

Hence ,

The required quadratic polynomial is x² + 5x + 6 .