Question

Find the nature of the roots of the quadratic equation: x +4x +5 =0​

Answer 1

Answer:

Step-by-step explanation:

x^2+4x+5 = 0

D=b^2-4ac

=16-4*5*1 = 16-20 = -4

Imaginary roots

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Answer 2

${Solution}$

Given Quadratic equation :-

• x² +4x + 5 = 0

To find :-

• Nature of the Quadratic equation

Solution:-

Nature of the Quadratic equation is determined by its Discriminant .It is denoted by D .Discriminant of a Quadratic equation is b² - 4ac There are some cases to determine the nature

Cases :-

• D = 0 Roots are real and equal
• D > 0 Roots are Real and Distinct
• D < 0 Roots are complex and conjugate

Finding Discriminant :-

$x {}^{2} + 4x + 5 = 0$

$a = 1 \:$

$b = 4$

$c = 5$

$discriminant \: = b {}^{2} - 4ac$

$= (4) {}^{2} - 4(1)(5)$

$16 - 20$

$- 4$

$d < 0$

Hence roots are complex and conjugate to each other

So, the roots of Quadratic equation x² + 4x + 5 is complex and conjugate to each other