Answer :

a = 19

Note:

★ The possible values of the variable which satisfy the equation are called its roots or solutions .

★ A QUADRATIC equation can have atmost two roots .

★ The general form of a quadratic equation is given as ; Ax² + Bx + C = 0

★ If α and ß are the roots of the quadratic equation Ax² + Bx + C = 0 , then ;

• Sum of roots , (α + ß) = -B/A

• PRODUCT of roots , (αß) = C/A

★ If α and ß are the roots of a quadratic equation , then that quadratic equation is given as : k•[ x² - (α + ß)x + αß ] = 0 , k ≠ 0.

★ The DISCRIMINANT , D of the quadratic equation Ax² + Bx + C = 0 is given by ;

D = B² - 4AC

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

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

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

Solution :

Here ,

The given quadratic equation is ;

(a-3)x² + 4(a-3)x + 4 = 0

Now ,

COMPARING the given quadratic equation with the general quadratic equation Ax² + Bx + C = 0 , we have ;

A = (a - 3)

B = (a - 3)

C = 4

Now ,

The discriminant of the given quadratic equation will be given as ;

=> D = B² - 4AC

=> D = (a - 3)² - 4×(a - 3)×4

=> D = (a - 3)² - 16(a - 3)

=> D = (a - 3)(a - 3 - 16)

=> D = (a - 3)(a - 19)

Now ,

The given quadratic equation will have equal roots if its discriminant is zero .

Thus ,

=> D = 0

=> (a - 3)(a - 19) = 0

=> a = 3 , 19

Here ,

a = 3 is rejected value , because if a = 3 , the given equation will no more be a quadratic equation .

Thus ,

a = 19 is appropriate value .

Hence ,

Required value of a is 19 .