Question

Assertion (A): The discriminant of the quadratic equation `x^2 + 2sqrt(2)x + 1 = 0` is less than zero.

Reason (R): The discriminant of the quadratic equation ax² + bx + c = 0 is `sqrt(b^2 - 4ac)`.

Options

• A is true, R is false

• A is false, R is true

• Both A and R are true

• Both A and R are false

Answer 1

Both A and R are false

Explanation:

For `x^2 + 2sqrt(2)x + 1 = 0`,

a = 1, b = `2sqrt(2)`, c = 1, 

So, discriminant Δ = b² – 4ac 

= `(2sqrt(2))^2 - 4(1)(1)`

= 8 – 4

= 4 (> 0) 

Thus, A (Δ < 0) is false.

R is false because the discriminant is the expression b² – 4ac itself; the quadratic formula uses `sqrt((b^2 - 4ac)`, but the discriminant is not the square root.