Question

СРОЧНО _(((НУЖНА НАЙТИ ДЕСКРИМИНАНТ И КОРНИ 1)4x^2+11-3<02)x^2-81<03)7x^2-4x+1>0c решением пожалуйста

Answer 1

1) 4x^2+8<0
4(x^2+2)=0
x^2+2=0
x^2=-2
корней нет
Ответ: решений нет
2) x^2-81<0
(x-9)(x+9)<0
x1=9  x2=-9
Ответ:(-9;9)
3) 7x^2-4x+1>0
7x^2-4x+1=0
D=16-28=-12
корней нет!
Ответ:x-любое число

Answer 2

Quadratic Inequalities and Discriminant

To solve the given quadratic inequalities and find the discriminant and roots, we'll follow a step-by-step approach.

Finding the Discriminant

The discriminant of a quadratic equation in the form of ax^2 + bx + c is given by the formula: Δ = b^2 - 4ac

For the first inequality, 4x^2 + 11x - 3 < 0, the coefficients are: - a = 4 - b = 11 - c = -3

Let's calculate the discriminant using the given coefficients: Δ = 11^2 - 4*4*(-3)

The discriminant for the first inequality is Δ = 121 + 48 = 169.

For the second inequality, x^2 - 81 < 0, the coefficients are: - a = 1 - b = 0 - c = -81

Calculating the discriminant: Δ = 0^2 - 4*1*(-81) The discriminant for the second inequality is Δ = 324.

For the third inequality, 7x^2 - 4x + 1 > 0, the coefficients are: - a = 7 - b = -4 - c = 1

Calculating the discriminant: Δ = (-4)^2 - 4*7*1 The discriminant for the third inequality is Δ = 16 - 28 = -12.

Finding the Roots

The nature of the roots of a quadratic equation can be determined based on the discriminant: - If Δ > 0, the equation has two distinct real roots. - If Δ = 0, the equation has exactly one real root. - If Δ < 0, the equation has no real roots.

Let's analyze the nature of the roots for each inequality based on the calculated discriminants.

Analyzing the Inequalities

1. For the inequality 4x^2 + 11x - 3 < 0: - Discriminant Δ = 169, which is greater than 0. - Therefore, the inequality has two distinct real roots.

2. For the inequality x^2 - 81 < 0: - Discriminant Δ = 324, which is greater than 0. - Hence, the inequality also has two distinct real roots.

3. For the inequality 7x^2 - 4x + 1 > 0: - Discriminant Δ = -12, which is less than 0. - Therefore, the inequality has no real roots.

Conclusion

- The solutions for the inequalities are as follows: 1. 4x^2 + 11x - 3 < 0 has two distinct real roots. 2. x^2 - 81 < 0 has two distinct real roots. 3. 7x^2 - 4x + 1 > 0 has no real roots.

Feel free to ask if you have further questions or need additional assistance!