Question

if a,b are the zeros of the
polynomial x2+6x+2 then
(1/a+1/b) are the zeroes of​

Answer 1

Question :

If α and ß are the zeros of the quadratic polynomial x² + 6x + 2 , then find ;

1/α + 1/ß .

Answer :

1/α + 1/ß = -3

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 ,

The given quadratic polynomial is ;

x² + 6x + 2 .

Comparing the given quadratic polynomial with the general quadratic polynomial ax² + bx + c , We have ;

a = 1

b = 6

c = 2

Now ,

=> Sum of zeros = -b/a

=> 1/α + 1/ß = -6/1

=> 1/α + 1/ß = -6

Also ,

=> Product of zeros = c/a

=> αß = 2/1

=> αß = 2

Now ,

=> 1/α + 1/ß = (ß + α)/αß

=> 1/α + 1/ß = (α + ß)/αß

=> 1/α + 1/ß = -6/2

=> 1/α + 1/ß = -3

Hence ,

1/α + 1/ß = -3 .