Discriminants and Hidden Quadratics

Discriminant

100

Determine the discriminant of the quadratic equation 2x^2 + 3x + 1 = 0

The discriminant is 1

200

Determine whether the equation x^3 - 3x^2 - x + 3 = 0 has any real roots.

Yes

300

What is the discriminant of the equation x^4 + 4x^3 + 10x^2 + 12x + 9 = 0?

324

400

What is the discriminant of the quadratic equation 12x^2 - 105x + 233 = 0?

19369

500

 Determine the discriminant of this function f(x) = 7x^2 + 900x + 12,526.

459,272

Hidden Quadratic

100

Solve for x: x^2 + √x = 9x

1

200

x² + 1 = 6  ÷ x²

x₁ = - √ 2 x₂ = √ 2

300

x-5√ x + 6 = 0 

x₁ = 4 x₂ = 9

400

Solve for x: √x + 4 = 16/x

 x= 12

500

x^2 + 3√x = 10/x^3

x= 1/2

Discriminant

100

Find the discriminant of the quadratic equation x^2 - 4x + 4 = 0

The discriminant is 0

200

Find the discriminant of 3x^2 + 5x - 2 = 0

49

300

Find the discriminant of 2x^2 + 3x + 7 = 0.

-83

400

Find the discriminant of 7x^2 - 6x + 93 = 0.

7896

500

Find the discriminant of the quadratic equation 3x^2 - 7x + 5/2 = 0

19

Hidden Quadratic

100

Solve the equation: x^2 + √x = 5x^3

0.25

200

Solve for x: √x^3 - 3 = 27x

-1, x = 4

300

x-6√ x + 5 = 0

x₁ =  5  x₂ = 25

400

Solve for x: √x + 7 = 15x

Answer: x = 1/15, x = 49/225

500

Solve the equation: x^3 + √x = 12/x^2

x = 2

Discriminant

100

Calculate the discriminant of the quadratic equation 3x² - 6x + 9 = 0

The discriminant is 0

200

Find the discriminant of x^2 - 8x + 67 = 0.

36

300

Find the discriminant of 4x^2 - 3x - 17 = 0

277

400

Find the discriminant of 3x^2 + 16x + 655 = 0

11,504

500

Find the discriminant of 5x^2 - 2x - 728 = 0

29,312