Question

Solve the following equations and choose the correct solution for each:

x ^2−10x=24

A) 7
B) 12
C) -2

2x^2 −11=87

A) 7
B) -7
C) 7

3x^2−12x+24=0

A) 1, 2 + 2i
B) 2, -2i
C) -21, √2

Answer 1

Quadratic equations are solved using the quadratic formula. This problem set contains three equations, each of which is solved by first bringing the equation into the standard form and then applying the quadratic formula or square root if applicable to find the solutions.

Step-by-step explanation:

Solving Quadratic Equations

Quadratic equations are in the form of ax^2+bx+c = 0. To solve these equations, we can use the quadratic formula, which is x = [-b ± sqrt(b^2 - 4ac)] / (2a). We'll solve each equation one by one.

1. For the equation x^2 - 10x = 24, first, we need to bring the equation to the standard quadratic form by subtracting 24 from both sides to get x^2 - 10x - 24 = 0. Now we can apply the quadratic formula by identifying a=1, b=-10, and c=-24.
2. The second equation, 2x^2 -11 = 87, simplify to 2x^2 = 98. We then divide by 2 and take the square root of both sides to find the solutions.
3. The third equation 3x^2 - 12x + 24 = 0 is already in the standard form. We use the quadratic formula with a=3, b=-12, and c=24 to find the solutions.