Quadratic Equations Challenge

Solve the quadratic equation: x^2 + 5x + 6 = 0

• x = -2, -3

• x = 2, 3

• x = -4, -5

• x = 1, -6

Find the roots of the equation: 2x^2 - 9x + 5 = 0

• x = (9 + √41) / 5, x = (9 - √41) / 5

• x = (9 + √41) / 2, x = (9 - √41) / 2

• x = (9 + √41) / 4, x = (9 - √41) / 4

• x = (9 + √41) / 3, x = (9 - √41) / 3

Determine the discriminant of the equation: 3x^2 + 4x - 2 = 0

• 10

• 25

• -16

• 40

Factorize the quadratic expression: x^2 - 9

• (x + 1)(x - 9)

• (x - 4)(x + 2)

• (x + 4)(x - 2)

• (x + 3)(x - 3)

Simplify the expression: (2x + 3)(x - 4)

• 2x^2 - 5x + 12

• 2x^2 + 5x - 12

• 2x^2 - 3x - 12

• 2x^2 - 5x - 12

What is the vertex form of the quadratic equation y = x^2 + 6x + 9?

• y = (x + 2)^2

• y = (x + 3)^2

• y = (x + 4)^2

• y = (x + 5)^2

Calculate the sum of the roots of the equation: 4x^2 - 12x + 9 = 0

• 3

• 6

• 2

• 5

Solve the inequality: x^2 - 4x > 5

• x < -1 or x > 5

• x > -1 and x < 5

• x > -1 or x < 5

• x < -1 or x < 5

Find the value of x in the equation: 2(x - 3)^2 = 32

• x = 5 or x = -2

• x = 10 or x = -5

• x = 4 or x = -3

• x = 7 or x = -1

Determine the nature of the roots of the equation: 5x^2 - 3x + 7 = 0

• The roots are rational

• The roots are imaginary

• The roots are irrational

• The discriminant of the equation 5x^2 - 3x + 7 = 0 is (-3)^2 - 4*5*7 = 9 - 140 = -131. Since the discriminant is less than 0, the roots are complex.