Question

Use the quadratic formula to solve the equation -3x2-x-3=0

Answer 1

Using quadratic formula, the solution to this equation is the roots of the equations given are ; x = 1+√35i / -6 or x = 1-√35i / -6

Explanation:

-3x² - x - 3=0

To solve this using quadratic formula, we will first of all write down the quadratic formula

x = -b ±√b²- 4ac / 2a

From the above question;

a = -3 b = -1 and c=-3

So we can now proceed to plug-in our variable

x = -(-1) ± √(-1)² - 4(-3)(-3) / 2(-3)

x= 1±√1-36 / -6

x = 1 ±√-35 / -6

x=1 ± √35 · √-1 /-6

x = 1±√35 i / -6

Note the square root of negative 1 is i

Either x = 1+√35i / -6 or x = 1-√35i / -6

Therefore the roots of the equations given are ; x = 1+√35i / -6 or x = 1-√35i / -6

Answer 2

`x=(1+√(35)i)/(-6)\,\, and\,\, x=(1-√(35)i)/(-6)\\`

Explanation:

the quadratic formula is:

`x=(-b\pm√(b^2-4ac))/(2a)`

a= -2, b = -1 and c =-3

Putting values in the formula

`x=(-(-1)\pm√((-1)^2-4(-3)(-3)))/(2(-3))\\x=(1\pm√(-35))/(-6)\\x=(1+√(-35))/(-6)\,\, and\,\, x=(1-√(-35))/(-6)\\We\,\, know \,\,that \,\,√(-1) = i  \\x=(1+√(35)i)/(-6)\,\, and\,\, x=(1-√(35)i)/(-6)\\`

So,
`x=(1+√(35)i)/(-6)\,\, and\,\, x=(1-√(35)i)/(-6)\\`