Question

X^2-12x+43 i need some help with this maths question

Answer 1

In order to solve a quadratic equation with one unknown, we need to factor it. If at first glance we can't find easy roots, we do a discrimination.

• 
  `f(x)=x^2-12x+43`
• Δ
  `f(x)=b^2-4ac=(-12)^2-4(43)`
• Δ
  `=-28`

If this value is less than zero, Δ
`< 0,` we determine that it has no solution belonging to the set of real numbers. We will find a conjugate and two complex roots. (
`a+bi`)

Let's use the following formulas to find the roots.

• 
  `x_(1)=(-b-√(D) )/(2a)= (12-√(-28) )/(2)=6-√(7)i`
• 
  `x_(2)=(-b-√(D) )/(2a)= (12+√(-28) )/(2)=6+√(7)i`

Complex Solutions:

1. 
   `6+√(7)i`
2. 
   `6-√(7)i`