Question

If a and B are the zeros of the quadratic polynomial f(x) = x² - 2x + 3, find the root of 1/alpha and 1/beta​

Answer 1

Answer :

1/α + 1/ß = 2/3

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.

★ The discriminant , D of the quadratic polynomial ax² + bx + c is given by ;

D = b² - 4ac

★ If D = 0 , then the zeros are real and equal .

★ If D > 0 , then the zeros are real and distinct .

★ If D < 0 , then the zeros are unreal (imaginary) .

Solution :

Here ,

The given quadratic polynomial is ;

f(x) = x² - 2x + 3

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

a = 1

b = -2

c = 3

Now ,

It is given that , α and ß are the zeros of the given quadratic polynomial f(x) .

Thus ,

=> Sum of zeros = -b/a

=> α + ß = -(-2)/1

=> α + ß = 2

Also ,

=> Product of zeros = c/a

=> αß = 3/1

=> αß = 3

Now ,

=> 1/α + 1/ß = (ß + α)/αß

=> 1/α + 1/ß = 2/3

Hence ,

1/α + 1/ß = 2/3