Question

Solve using Formula method :- x2

+ x + 5 = 0​

Answer 1

Answer:

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Answer 2

Answer:

x = ((-1) + i√19)/2 or x = ((-1) - i√19)/2

Step-by-step explanation:

We have,

x² + x + 5 = 0

ax² + bx + c = 0

where a = 1, b = 1, c = 5

Now,

The Quadratic formula = (-b ± √(b² - 4ac))/2a

Here,

x = (-(1) ± √((1)² - 4(1)(5))/2(1)

x = (-1 ± √(1 - 20))/2

x = (-1 ± √(-19))/2

Here we have a negative number inside the root, this means that the roots of this Quadratic equation will be a complex number.

We know that,

6² = 36

(-6)² = 36

But what number gives a -ve value, when multiplied by itself, well we do not know, so we call this number as an imaginary number and denote it with 'i'.

Now,

√(-19) = √(19 × (-1))

√(19 × (-1)) = √19 × √(-1)

Now,

we can say that, √(-1) = i

∴ x = ((-1) ± √19 × i)/2

x = ((-1) ± i√19)/2

Hence,

x = ((-1) + i√19)/2 or x = ((-1) - i√19)/2

Hope it helped and believing you understood it........All the best