Question

Find the discriminant of the equation x2 -3x-2=0 and hence find the nature of the roots
Plzz help!!

Answer 1

x²-3x-2 = 0

D = b²-4ac
= (-3)²-4*1*(-2)
= 9+8
= 17

x = (-b±√D)/2a
= -(-3)±√17/2*1
= 3±√17/2
hence, the roots are 3+√17/2 and 3-√17/2

Answer 2

Given : The quadratic equation is, x²-3x-2 = 0

To find : The discriminant of the equation and the nature of the roots.

Solution :

We can simply solve this mathematical problem by using the following mathematical process. (our goal is to calculate the discriminant and the nature of the roots)

If, there's a quadratic equation :

ax²+bx+c = 0

Then, its discriminant = b²-4ac

Comparing the given quadratic equation x²-3x-2 = 0 with the standard form of quadratic equation (i.e. ax²+bx+c = 0) we get :

• a = 1
• b = -3
• c = -2

So, the discriminant will be :

= b²-4ac

= (-3)² - [4 × 1 × (-2)]

= 9 - (-8)

= 9 + 8

= 17

The discriminant is greater than zero and the discriminant is not a perfect square.

So, the roots will be real, unequal and irrational.

Hence, the discriminant of the equation x²-3x-2 = 0 is 17. The roots are real, unequal and irrational.