Question

The roots of the quadratic equation x² + x − 1 = 0  are ______.

विकल्प

• Irrational and distinct

• not real

• rational and distinct

• real and equal

Answer 1

The roots of the quadratic equation x² + x − 1 = 0 are irrational and distinct.

Explanation:

Here a = 1, b = 1, c = −1

Discriminant (D) = b² − 4ac

= (1)² − 4 × 1 (−1)

= 1 + 4

= 5

Since D > 0

There are 2 distinct real roots.

Now using quadratic formula to find roots

x = `(-b +- sqrt D)/(2a)`

Putting values

x = `(-1 +- sqrt 5)/(2 xx 1)`

x = `(-1 +- sqrt 5)/(2)`

Therefore, the roots of the quadratic equation x² + x − 1 = 0 are x = `(-1 + sqrt 5)/(2 xx 1)` and x = `(-1 - sqrt 5)/(2 xx 1)`

Thus,

Roots are irrational and distinct0