Question

Which of the following are solutions?

Answer 1

This is a quadratic equation. There's a shortcut (two shortcuts really) called the Shakespeare Quadratic Formula (2b or -2b) applicable when the middle term is even:

`x^2 - 2bx + c \textrm{ has zeros } x= b\pm √(b^2-c)`

`ax^2 - 2bx + c \textrm{ has zeros } x= \frac 1 a( \left b\pm √(b^2-ac) \right)`

OK, our problem is

`9x^2 - 6x -7 = 0`

`x = \frac 1 9 (3 \pm √(9-(9)(-7))) = \frac 1 9(3 \pm √(72))= \frac 1 9(3 \pm 3 √(8)) = \frac 1 3(1 \pm \sqrt 8)`

Typically we'd write
`\sqrt 8 = 2 \sqrt 2` but the answers here don't so we won't either.

Answer: C and D