Question

If one of the zeroes of ax^2 + (a-4)x + 3,is the reciprocal of the other, then find 'a'​

Answer 1

Answer :

a = 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 ;

ax² + (a - 4)x + 3

Comparing the given quadratic polynomial with the general quadratic polynomial ,

We have ;

A = a

B = a - 4

C = 3

Also ,

It is given that , the zeros of the given quadratic polynomial are reciprocal of one another .

This ,

Let α and 1/α be the zeros of the given quadratic polynomial .

Now ,

=> Product of zeros = C/A

=> α × 1/α = 3/a

=> 1 = 3/a

=> a = 3

Hence , a = 3