Question

How many real roots are in 10x^2 +3x+6=0

Answer 1

0

Explanation:

Use the discriminant formula for parabola

`{b}^(2) - 4ac`

`{3}^(2) - 4(10)(6)`

`9- 240`

`- 231`

Since the answer is negative, we will have 2 imaginary roots so we won't have any real roots

Answer 2

No Real Roots

Explanation:

Hello!

To determine the types of roots a quadratic has, we can use the Discriminant.

Refer to the quadratic formula:
`x = \frac{-b\pm \sqrt{\bold{b^2 - 4ac}}}{2a}`

The bolded part (b² - 4ac) is the Discriminant.

Determining the roots

• Positive Discriminant gives us 2 roots that are real (can be rational or irrational)
• Zero Discriminant gives us 1 root that is real and rational (can also be known as a double root)
• Negative Discriminant gives us 2 roots that are not real, or imaginary.

We can plug in our values from the quadratic into the Discriminant Formula b² - 4ac.

Solve

• 
  `b^2 - 4ac`
• 
  `3^2 - 4(10)(6)`
• 
  `9 - 240`
• 
  `-231`

Since the discriminant is negative, there are two imaginary roots, or roots that don't exist.

The are no real roots for this quadratic.