Question

If a, ß are the zeros of the
polynomial f(x) = x2 + x + 1 = , then
1/a + 1/B
3:42 pm​

Answer 1

Answer :

1/α + 1/ß = -1

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 ;

f(x) = x² + x + 1 .

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

We have ;

a = 1

b = 1

c = 1

Also ,

It is given that , α and ß are the zeros of the given quadratic polynomial .

Thus ,

=> Sum of zeros = -b/a

=> α + ß = -1/1

=> α + ß = -1

Also ,

=> Product of zeros = c/a

=> αß = 1•1

=> αß = 1

Now ,

=> 1/α + 1/ß = (ß + α)/αß

=> 1/α + 1/ß = (α + ß)/αß

=> 1/α + 1/ß = -1/1

=> 1/α + 1/ß = -1

Hence , 1/α + 1/ß = -1 .

Answer 2

Given :-

• Quadratic Polynomial : f(x) = x²+x+1.

To Find :-

• The value of 1/α + 1/β .

Solution :-

Given that, f(x) = x² + x + 1.

On comparing with ax² + bx + c , We get :

↪ a = 1 , b = 1 , c = 1

Given that, α and β are the zeroes of the polynomial.

↪ Sum of roots = -b/a

↪ α + β = -1/1

↪ α + β = -1

↪Product of roots = c/a

↪ αβ = 1/1

↪ αβ = 1

Now, we need to find out the value of 1/α + 1/β.

↪ 1/α + 1/β = α+β/αβ

↪ 1/α + 1/β = -1/1

↪ 1/α + 1/β = -1

Hence,

• The value of 1/α + 1/β is -1.