Question

Найти дискреминант 3x²+8x-4<0

Answer 1

Д= 8 в квадрате- 4×3×(-4)

Answer 2

To find the discriminant for the quadratic inequality $3x^2 + 8x - 4 < 0$, we first need to identify the quadratic equation associated with the inequality.

The general form of a quadratic equation is $ax^2 + bx + c = 0$. In this case, our quadratic equation is $3x^2 + 8x - 4$.

Now, let's find the discriminant, denoted by $D$, which is given by the formula $D = b^2 - 4ac$ for a quadratic equation $ax^2 + bx + c = 0$.

For our equation $3x^2 + 8x - 4$, we have:

$a = 3$, $b = 8$, $c = -4$.

Now, calculate the discriminant:

$D = (8)^2 - 4 \cdot 3 \cdot (-4)$ $D = 64 + 48$ $D = 112$

So, the discriminant of the quadratic equation is $D = 112$.

To analyze the nature of the roots and the inequality, we can use the value of the discriminant:

1. If $D > 0$, the quadratic equation has two distinct real roots, and the inequality holds true for the values of $x$ between those two roots.
2. If $D = 0$, the quadratic equation has one real root (a repeated root), and the inequality holds true for that particular value of $x$.
3. If $D < 0$, the quadratic equation has no real roots, and there are no values of $x$ for which the inequality holds true.

In this case, since $D = 112 > 0$, the quadratic equation has two distinct real roots, and the inequality $3x^2 + 8x - 4 < 0$ holds true for the values of $x$ between those two roots.