Question

Solve 5x^2 − 3x + 17 = 9.

Answer 1

The roots of the equation are x =
`(3+√(151)i)/(10)` and x =
`(3-√(151)i)/(10)`

and there are no real roots of the equation given above

Explanation:

To solve:

5x² − 3x + 17 = 9

or

⇒ 5x² − 3x + 17 - 9 = 0

or

⇒ 5x² − 3x + 8 = 0

Now,

the roots of the equation in the form ax² + bx + c = 0 is given as:

x =
`(-b\pm√(b^2-4ac))/(2a)`

in the above given equation

a = 5

b = -3

c = 8

therefore,

x =
`(-(-3)\pm√((-3)^2-4*5*8))/(2*5)`

or

x =
`(3\pm√(9-160))/(10)`

or

x =
`(3+√(-151))/(10)` and x =
`(3-√(-151))/(10)`

or

x =
`(3+√(151)i)/(10)` and x =
`(3-√(151)i)/(10)`

here i = √(-1)

Hence,

The roots of the equation are x =
`(3+√(151)i)/(10)` and x =
`(3-√(151)i)/(10)`

and there are no real roots of the equation given above