Question

Дискриминант(-ы) 4x^4-17x^2+4=0; (x^2-2x)^2 + (x^2-2x)=12; (2x^2+x-1)(2x^2+x-4)+2=0

Answer 1

Последний у меня не получился

Answer 2

Let's solve each quadratic equation separately and find the discriminants:

1. Quadratic equation: 4x^4 - 17x^2 + 4 = 0

To find the discriminant (D) of this equation, we use the formula: D = b^2 - 4ac

Here, a = 4, b = -17, and c = 4

D = (-17)^2 - 4 * 4 * 4 = 289 - 64 = 225

2. Quadratic equation: (x^2 - 2x)^2 + (x^2 - 2x) = 12

Let's simplify this equation first:

x^4 - 4x^3 + 4x^2 + x^2 - 2x - 12 = 0

x^4 - 4x^3 + 5x^2 - 2x - 12 = 0

To find the discriminant, we use the same formula: D = b^2 - 4ac

Here, a = 1, b = -4, and c = 5

D = (-4)^2 - 4 * 1 * 5 = 16 - 20 = -4

3. Quadratic equation: (2x^2 + x - 1)(2x^2 + x - 4) + 2 = 0

Let's expand the equation first:

4x^4 + 2x^3 - 4x^2 + 2x^3 + x^2 - 2x - 8x^2 - 4x + 16 + 2 = 0

4x^4 + 4x^3 - 12x^2 - 6x + 18 = 0

To find the discriminant, we use the same formula: D = b^2 - 4ac

Here, a = 4, b = 4, and c = -12

D = (4)^2 - 4 * 4 * (-12) = 16 + 192 = 208

So, the discriminants for the three equations are as follows:

1. 4x^4 - 17x^2 + 4 = 0: Discriminant (D) = 225
2. (x^2 - 2x)^2 + (x^2 - 2x) = 12: Discriminant (D) = -4
3. (2x^2 + x - 1)(2x^2 + x - 4) + 2 = 0: Discriminant (D) = 208