Question

X 2 +3x−4=x, squared, plus, 3, x, minus, 4, equals

Answer 1

Explanation:

Step 1: Identify the coefficients.

The equation is in the form
`\(ax^2 + bx + c = 0\)`.

Here,
`\(a = 1\)`,
`\(b = 3\)`, and
`\(c = -4\)`.

Step 2: Calculate the discriminant.

The discriminant,
`\( \Delta \)`, is given by the formula:

`\[ \Delta = b^2 - 4ac \]`

Plugging in the values we have:

`\[ \Delta = 3^2 - 4(1)(-4) \]`

`\[ \Delta = 9 + 16 \]`

`\[ \Delta = 25 \]`

Step 3: Use the quadratic formula.

The solutions for \(x\) are given by:

`\[ x_1 = (-b + √(\Delta))/(2a) \]`

`\[ x_2 = (-b - √(\Delta))/(2a) \]`

Using the values for
`\(a\)`,
`\(b`, and
`\( \Delta \)` we found:

`\[ x_1 = (-3 + 5)/(2) = 1 \]`

`\[ x_2 = (-3 - 5)/(2) = -4 \]`

Solution:

The equation
`\(x^2 + 3x - 4 = 0\)` has two solutions:

`\[ x_1 = 1 \]`

`\[ x_2 = -4 \]`