Question

How many real roots does the equation have?


x^2 + 3x + 4 = 0​

Answer 1

Answer:

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Answer 2

The equation does not have any real root.

Given:

The quadratic equation: $x^{2} +3x+4=0$

To Find:

If the quadratic equation has any real roots.

Solution:

Consider the general form of quadratic equation:

$ax^{2} + bx + c =0$

The roots of the equation is given by the formula:

±$\frac{\sqrt{b^{2} - 4ac } }{2a}$

Comparing  $x^{2} +3x+4=0$ with $ax^{2} + bx + c =0$;

a = 1

b = 3

c = 4

Now, the roots of the equation are:

±$\frac{\sqrt{9-16} }{2}$

=>± $\frac{\sqrt{-7} }{2} }$

The roots of the equations are : 7i/2 and -7i/2 .

Hence, there are no real roots of the given quadratic equation.

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