Question

find the nature of roots of the quadratic equation x^2+3x-4=0​

Answer 1

Answer: real and distinct roots

Step-by-step explanation:

Discriminant =(b^2)-4 a

So we get discriminant equal to 25

We know that it discriminant is greater than zero than the nature of roots are real and distinct

Answer 2

Given: $\sf x^2\ +\ 3x -\ 4\ =\ 0.$

To find: The nature of its roots.

Answer:

In order to find the nature of the roots of an equation, we solve its discriminant (D).

If  $\sf ax^2\ +\ bx\ + c\ =\ 0$  were an equation, its discriminant would be given by:

                                                   $\bf b^2\ -\ 4ac$

From the given equation (in the question), the respective values would be:

• a = 1
• b = 3
• c = - 4

Now, conditions to determine the nature.

• If $\sf b^2\ -\ 4ac\ =$  0, the equation has real roots.
• If $\sf b^2\ -\ 4ac$   <  0, the equation has no real roots.

• If $\sf b^2\ -\ 4ac$   >  0, the equation has real and distinct roots.

Let's now solve the discriminant of the given equation.

From the given equation,

Using the values we mentioned above,

$\sf b^2\ -\ 4ac\ =\ (3)^2\ -\ 4\ \times\ 1\ \times\ (-4)\\\\\\D\ =\ 9\ +\ 16\\\\\\D\ =\ 25$

Since the discriminant (D) appears to be more than 0, the equation has real and distinct roots.