Question

Use the Quadratic formula to solve the equation. Show your work.

3x^2 + 2x + 1 = 0

Answer 1

`x=(-1 +√(2)\:i )/(3), \quad x=(-1 -√(2)\:i )/(3)`

Explanation:

Quadratic Formula

`x=(-b \pm √(b^2-4ac) )/(2a)\quad\textsf{when }\:ax^2+bx+c=0`

Given quadratic equation:

`3x^2+2x+1=0`

Therefore:

• a = 3
• b = 2
• c = 1

Substitute the values of a, b and c into the quadratic formula and solve for x:

`\implies x=(-2 \pm √(2^2-4(3)(1)) )/(2(3))`

`\implies x=(-2 \pm √(4-12) )/(6)`

`\implies x=(-2 \pm √(-8) )/(6)`

`\implies x=(-2 \pm √(4\cdot2\cdot-1) )/(6)`

`\implies x=(-2 \pm √(4)√(2)√(-1) )/(6)`

`\implies x=(-2 \pm 2√(2)\:i )/(6)`

`\implies x=(-1 \pm √(2)\:i )/(3)`

Imaginary Number Rule

`\boxed{√(-1)=i}`