Question

How many real number solutions are there to the equation 0 = 4x² + 3x + 2 ?

Answer 1

Using the quadratic formula, let's determine the solution of the following equation:

`\text{ 4x}^2\text{ + 3x + 2 = 0}`

We get,

a = 4, b = 3 and c = 2

`\text{ x = }\frac{\text{ -b }\pm\text{ }\sqrt{\text{b}^2\text{ - 4ac}}}{\text{2a}}`
`\text{ x = }\frac{-(3)\text{ }\pm\text{ }\sqrt{(3)^2\text{ - 4\lparen4\rparen\lparen2\rparen}}}{2(4)}\text{ = }\frac{-3\text{ }\pm\text{ }\sqrt{9\text{ - 32}}}{8}`
`\text{ x = }\frac{-3\text{ }\pm\text{ }√(-23)}{8}`
`\text{ x}_1=\text{ }\frac{-3\text{ + }√(-23)}{8}\text{ = }\frac{-3\text{ + i}√(23)}{8}\text{ \lparen imaginary\rparen}`
`\text{ x}_2\text{ = }\frac{-3\text{ - }√(-23)}{8}\text{ = }\frac{-3\text{ - i}√(23)}{8}\text{ \lparen imaginary\rparen}`

Therefore, the equation has 2 imaginary roots and no real number solutions.

The answer is 0.