Question

I need help with this algebra 2

Answer 1

Answer:

(2)

Step-by-step explanation:

2(2x-1) = 5x²

expand

4x - 2 = 5x²

subtract (4x-2) from both sides to make it a quadratic equation

5x² -4x + 2 = 0

plug into the quadratic formula

ax² + bx + c

$x= \frac{-b+-\sqrt{b^2-4ac} }{2a} \\= \frac{-(-4)+-\sqrt{(-4)^2-4(5)(2)} }{2(5)} \\= \frac{4+-\sqrt{16-40} }{10} \\= \frac{4+-\sqrt{-24} }{10} \\\\=\frac{4+-2i\sqrt{6(4)(-1)} }{10} \\= \frac{4+-2i\sqrt{6} }{10} \\= \frac{2+-i\sqrt{6} }{5} \\= 2/5 +- \sqrt{6} /5 * i$

thus, the coefficient attached to i is +- √6/5, making (2) our answer

(1) is not the answer because our answer would then be

a + bi = 2/5 + √6/5 * i * i = 2/5 - √6/5, which isn't our answer