Question

What are the roots of x2 + 10x + 29 = 0?

Answer 1

x² + 10x + 29 = 0
x = -(10) ± √((10)² - 4(1)(29))
2(1)
x = -10 ± √(100 - 116)
2
x = -10 ± √(-16)
2
x = -10 ± 4i
2
x = -5 ± 2i
x = -5 + 2i or x = -5 - 2i

THe roots of the function is 5 ± 2i.

Answer 2

The roots of the given equation are -5 + 2i and -5 - 2i

Explanation:

Since, roots of an equation are the points which satisfy the equation,

Or the points which are obtained after solving the equation. ( by putting zero on right side )

Here, the given quadratic equation,

`x^2+10x+29=0`

If we have an equation, ax² +bx + c = 0

By quadratic formula,

`x=\frac{-b\pm \sqr{b^2-4ac}}{2a}`

By comparing,

The solution of the given equation is,

`x=(-10\pm √(10^2-4* 1* 29))/(2* 1)`

`x=(-10\pm √(100-116))/(2)`

`x=(-10\pm √(-16))/(2)`

`x=(-10\pm +4i)/(2)`

`\implies x = -5\pm 2i`

Thus, the roots of the given equation are -5 + 2i and -5 - 2i