Question

X²-3х-4=0 Решите через дискрименант, пожалуйста)))

Answer 1

D=9+16=25
x1=(3+5):2=4
x2=(3-5):2=-1

Answer 2

Solving the Quadratic Equation using the Discriminant

To solve the equation x² - 3x - 4 = 0 using the discriminant, we need to first identify the coefficients of the quadratic equation. In this case, a = 1, b = -3, and c = -4.

The discriminant (Δ) is calculated using the formula: Δ = b² - 4ac.

Substituting the values, we have: Δ = (-3)² - 4(1)(-4).

Calculating the discriminant, we get: Δ = 9 + 16 = 25.

Now, let's analyze the value of the discriminant to determine the nature of the roots:

- If Δ > 0, the equation has two distinct real roots. - If Δ = 0, the equation has one real root (a repeated root). - If Δ < 0, the equation has no real roots (complex roots).

In this case, since Δ = 25 > 0, the equation has two distinct real roots.

To find the roots, we can use the quadratic formula: x = (-b ± √Δ) / (2a).

Substituting the values, we have: x = (-(-3) ± √25) / (2(1)).

Simplifying further, we get: x = (3 ± 5) / 2.

Therefore, the two solutions to the equation x² - 3x - 4 = 0 are:

- x₁ = (3 + 5) / 2 = 8 / 2 = 4 - x₂ = (3 - 5) / 2 = -2 / 2 = -1

So, the roots of the equation are x = 4 and x = -1.

Please let me know if there's anything else I can help you with!