Question

5x²-15x=0 решить нужно через дискриминант

Answer 1

Відповідь:

x₁ = 0

x₂ = 3

Пояснення:

5x² - 15x = 0

D = 225 - 4*5*0 = 225

√D = 15

x₁ = 15 - 15/2*5 = 0/10 = 0

x₂ = 15 + 15/2*5 = 30/10 = 3

Answer 2

To solve the quadratic equation $5x^2 - 15x = 0$ using the discriminant, we first need to identify the coefficients of the equation: $a = 5$, $b = -15$, and $c = 0$.

The discriminant ($D$) of a quadratic equation $ax^2 + bx + c = 0$ is given by the formula: $D = b^2 - 4ac$.

Now, we can proceed with the steps:

Step 1: Calculate the discriminant ($D$). $D = (-15)^2 - 4 \cdot 5 \cdot 0$ $D = 225 - 0$ $D = 225$

Step 2: Analyze the discriminant to determine the nature of the roots.

• If $D > 0$, the equation has two distinct real roots.
• If $D = 0$, the equation has one real root (a repeated root).
• If $D < 0$, the equation has no real roots (two complex conjugate roots).

Step 3: Calculate the roots using the quadratic formula, which is given by $x = \frac{-b \pm \sqrt{D}}{2a}$.

In our case, $a = 5$, $b = -15$, and $D = 225$.

Step 4: Calculate the roots.

$x = \frac{-(-15) \pm \sqrt{225}}{2 \cdot 5}$

$x = \frac{15 \pm 15}{10}$

Now, we have two possibilities:

$x_1 = \frac{15 + 15}{10} = \frac{30}{10} = 3$

$x_2 = \frac{15 - 15}{10} = \frac{0}{10} = 0$

Step 5: Write down the solutions.

The quadratic equation $5x^2 - 15x = 0$ has two solutions: $x = 3$ and $x = 0$.