Question

9) If the product of zeroes of the polynomial ax 2 – 6x – 6 is 4, find the value of ‘a’.

Answer 1

Answer :

a = 3/2

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 - 6x - 6

Comparing the given quadratic polynomial with the general quadratic polynomial ,

We have ;

A = a

B = -6

C = 6

Also ,

It is given that , sum of the zeros of the given quadratic polynomial is 4 .

Now ,

=> Sum of zeros = -B/A

=> 4 = -(-6)/a

=> 4 = 6/a

=> a = 6/4

=> a = 3/2

Hence , a = 3/2