Question

Найти f(x)=0f(x)= -0.5x^2-4x+0.1 f(x)=x^2+x+1 f(x)-3x^2-4x

Answer 1

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Answer 2

To find the roots of the given functions, we need to solve for f(x) = 0. The roots of a function are the values of x for which f(x) equals zero.

1. f(x) = -0.5x^2 - 4x + 0.1:

To find the roots of this quadratic function, we can use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / 2a

where a = -0.5, b = -4, and c = 0.1.

x = (4 ± √((-4)^2 - 4(-0.5)(0.1))) / 2(-0.5) x = (4 ± √(16 + 0.2)) / -1 x = (4 ± √16.2) / -1 x = (4 ± 4.0249) / -1

So, the roots of f(x) = -0.5x^2 - 4x + 0.1 are: x₁ ≈ -0.0249 x₂ ≈ -7.9751

2. f(x) = x^2 + x + 1:

To find the roots of this quadratic function, we can again use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / 2a

where a = 1, b = 1, and c = 1.

x = (-1 ± √(1^2 - 4(1)(1))) / 2(1) x = (-1 ± √(1 - 4)) / 2 x = (-1 ± √(-3)) / 2

Since the discriminant (b^2 - 4ac) is negative, the roots of this quadratic equation are complex numbers.

x₁ ≈ (-1 + √3i) / 2 x₂ ≈ (-1 - √3i) / 2

3. f(x) = 3x^2 - 4x:

To find the roots of this quadratic function, we set f(x) equal to zero:

3x^2 - 4x = 0

Now, we can factor out the common term x:

x(3x - 4) = 0

Now, we have two possible roots:

1. x = 0
2. 3x - 4 = 0

For the second equation, we solve for x:

3x - 4 = 0 3x = 4 x = 4/3

So, the roots of f(x) = 3x^2 - 4x are: x₁ = 0 x₂ = 4/3