Question

find the roots of the quadratic equation x2+4x+5=0 by using quadratic formula​

Answer 1

$\huge{ \underline{ \underline{ \bold{required \: answer}}}}$

we have,

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

it's a quadratic equation..so it is in the form of

${ax}^{2} + bx + c = 0 \: \:(a ≠ 0)$

here,

• a = 1
• b = 4
• c = 5

quadratic formula;

$x = \frac{ - b \: ± \sqrt{D }}{2a} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ { \tt here } \:D { \tt\: is \: discriminant \: of \: the \: equation } \\ \\ { \tt \: and} \: \: D = {b}^{2} - 4ac \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

now, Let D be the discriminant of the equation x² + 4x + 5

Then,

$D = {b}^{2} - 4ac \: \:\\ \\ \implies D = {(4)}^{2} - 4 \times 1 \times 5 \\ \\ \implies D = 16 - 20 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \implies D = - 4 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

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★ first we have to know some things about roots of a quadratic equation:

☞︎︎︎ The quadratic equation ax² + bx + c = 0 , a ≠ 0 has;

1. two distinct real roots, if D = b²- 4ac > 0
2. two equal roots i.e. coincident real roots, if D = b² - 4ac = 0
3. no real roots, if D = b² - 4ac < 0

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and here, D = - 4

➪ D < 0

hence, the given quadratic equation has no real roots