Question

Let r and s be the roots of x^2 - 6x + 2 = 0. Find (r - s)^2.

Answer 1

Answer: $(r-s)^{2} = 28$

Step-by-step explanation:

• $x^{2} -6x+9=-2+9$
• $(x-3)^{2}=7$
• $(x-3)= -\sqrt{7}$ or $\sqrt{7}$ <-- there's no plus/minus sign.

• $(x-3) = -\sqrt{7}$
• $x = 3 -\sqrt{7}$ <-- root.

• $(x-3) = \sqrt{7}$
• $x = 3+\sqrt{7}$ <-- root.

• $[(3-\sqrt{7})-(3+\sqrt{7})]^{2}$
• $(3-\sqrt{7} -3 - \sqrt{7})^{2}$ <-- don't forget to distribute the negative.
• $(-2\sqrt{7})^{2}$
• $(4)(7)$
• $28$