Question

Find the nature of roots of equation 4x^2 - 2x - 1 = 0​

Answer 1

Step-by-step explanation:

4x^2-2x-1=0

4x^2-2x=1

2x(2x-1)=1

Answer 2

Given,

A quadratic equation: 4x^2 - 2x - 1 = 0

To find,

The nature of roots of the given quadratic equation.

Solution,

We can simply solve this mathematical problem using the following process:

Mathematically,

In a quadratic equation: ax^2 + bx + c = 0, the nature of its roots is determined by the value of discriminant D = (b^2-4ac), as follows:

a) if D>0, then real and distinct roots

b) if D=0, then real and equal roots

c) if D<0, then complex and distinct roots

{Statement-1}

According to the question,

The given quadratic equation:

4x^2 - 2x - 1 = 0

=> (4)x^2 + (-2)x + (-1) = 0

For the given quadratic equation, the value of:

a = 4

b = (-2)

c = (-1)

So, according to statement-1, the value of discriminant D is:

D = (b^2-4ac)

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

= 4 + 16 = 20 > 0

=> the given quadratic equation has two real and distinct roots

Hence, the given quadratic equation has two real and distinct roots.