Question

The discriminant of the quadratic equation in x namely [ax^2 - (a + 1)x + 1 ] = 0 is

Answer 1

Answer:

(a - 1)²

Note:

★ The general form of a quadratic equation is Ax² + Bx + C = 0 .

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

D = B² - 4AC

Solution:

Here,

The given quadratic equation is ;

ax² - (a + 1)x + 1 = 0

Clearly,

A = a

B = -(a + 1)

C = 1

Thus,

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

=> D = B² - 4AC

=> D = [-(a + 1)]² - 4•a•1

=> D = a² + 2a + 1 - 4a

=> D = a² - 2a + 1

OR

=> D = (a - 1)²

Hence,

The required answer is :

(a - 1)²