Question

What is x^2 + 2x + 4 = 0?

Answer 1

Given :- find the nature of the roots of x² + 2x + 4 = 0

Answer :-

we know that, If Ax² + Bx + C = 0 ,is any quadratic equation, then its discriminant is given by ,

• D = B² - 4AC .
• If D = 0 , then the given quadratic equation has real and equal roots .
• If D > 0 , then the given quadratic equation has real and distinct roots .
• If D < 0 , then the given quadratic equation has unreal (imaginary) roots .

So, comparing x² + 2x + 4 = 0 with Ax² + Bx + C = 0 we get,

• A = 1
• B = 2
• C = 4

then,

→ D = B² - 4AC

→ D = (2)² - 4*1*4

→ D = 4 - 16

→ D = (-12)

→ (-12) < 0 .

→ D < 0 .

therefore, we can conclude that , the given quadratic equation has unreal (imaginary) roots .

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Answer 2

SOLUTION

TO DETERMINE

Type of the equation

$\sf{ {x}^{2} + 2x + 4 = 0}$

CONCEPT TO BE IMPLEMENTED

Quadratic Equation

A quadratic equation is an algebraic equation consisting of variables and constants and equality sign in which the highest power of its variable that appears with nonzero coefficient is two

General form of a quadratic equation

The general quadratic equation is of the form

$\sf{a {x}^{2} + bx + c = 0 \: \: \: \: \: \: where \: a \ne \: 0}$

EVALUATION

Here the given equation is

$\sf{ {x}^{2} + 2x + 4 = 0}$

The variable is x

Now the equation is of the form

$\sf{a {x}^{2} + bx + c = 0 \: \: \: \: \: \: where \: a \ne \: 0}$

In the equation the highest power of its variable that appears with nonzero coefficient is two

So the equation is a quadratic equation

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