Question

If alpha and beta are the zeros of the polynomial x2+5x+8 then alpha× beta is

Answer 1

Answer :

αß = 8

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

Solution :

Here ,

The given quadratic polynomial is ;

x² + 5x + 8

Now ,

Comparing the given quadratic polynomial with the general quadratic polynomial ax² + bx + c , we get ;

a = 1

b = 5

c = 8

Also ,

It is given that , α and ß are the zeros of the quadratic polynomial ax² + bx + c .

Thus ,

=> Product of zeros = c/a

=> αß = 8/1

=> αß = 8

Hence , αß = 8 .