# Use the discriminant and select whether the roots of 5x^{2} - 4x + 3 = 0 are real or non-real.

A quadratic equation is in the form of ax^{2} + bx + = 0. We can calculate the roots of the quadratic equation using the roots of quadratic equation calculator.

## Answer: The roots for the equation 5 x^{2} + 4x + 3 = 0 are non real since the value of the discriminant D = -44 < 0.

Let's find the value of discriminant and nature of roots.

**Explanation:**

To find the nature of roots of a quadratic equation we will find the discriminant.

The discriminant is given by D = b^{2} - 4 ac

- If D > 0, the equation has two real and distinct roots
- If D = 0, the equation has real and equal roots.
- If D < 0, the equation has no real roots or complex roots.

Where a = coefficient of x^{2}, b = coefficient of x and c = constant term.

Now, consider the given equation 5x^{2} - 4x + 3 = 0

a = 5, b = -4, c = 3

Let's check for the discriminant b^{2} - 4 ac as shown below

⇒ (- 4) ^{2} - 4 × (5) × (3)

⇒ 16 - 4 × (15)

⇒ 16 - ( 60 )

⇒ - 44

Since - 44 < 0 → The equation has no real roots.

### Thus, The roots for the equation 5 x^{2} + 4 x + 3 = 0 are non real.

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