Question

X2+9x+18 verify the relation between roots and coefficients

Answer 1

Ответ:

Пошаговое объяснение:

To verify the relation between the roots and coefficients of the quadratic equation x^2 + 9x + 18 = 0, we can use Vieta's formulas. Vieta's formulas state that for a quadratic equation in the form ax^2 + bx + c = 0, the sum of the roots is equal to -b/a, and the product of the roots is equal to c/a.

In this case, the coefficients of the equation are:

a = 1

b = 9

c = 18

According to Vieta's formulas:

Sum of the roots = -b/a = -9/1 = -9

Product of the roots = c/a = 18/1 = 18

Therefore, the sum of the roots of the equation x^2 + 9x + 18 = 0 is -9, and the product of the roots is 18.

Answer 2

The relationship between the roots of a quadratic equation of the form `ax^2 + bx + c = 0` and its coefficients (`a`, `b`, and `c`) is described by Vieta's formulas. Vieta's formulas provide a connection between the roots and coefficients of a quadratic equation. In your case, the equation is `x^2 + 9x + 18 = 0`, where `a = 1`, `b = 9`, and `c = 18`.

Vieta's formulas state that for a quadratic equation of the form `ax^2 + bx + c = 0` with roots `x1` and `x2`, the following relationships hold:

1. The sum of the roots `x1` and `x2` is equal to the negation of the coefficient of the linear term `b` divided by the coefficient of the quadratic term `a`: `x1 + x2 = -b/a`

2. The product of the roots `x1` and `x2` is equal to the constant term `c` divided by the coefficient of the quadratic term `a`: `x1 * x2 = c/a`

In your equation, `a = 1`, `b = 9`, and `c = 18`, so we can apply Vieta's formulas:

1. The sum of the roots `x1` and `x2` is given by: `x1 + x2 = -b/a = -9/1 = -9`

2. The product of the roots `x1` and `x2` is given by: `x1 * x2 = c/a = 18/1 = 18`

So, for the equation `x^2 + 9x + 18 = 0`, the sum of its roots is -9, and the product of its roots is 18. These relationships are consistent with Vieta's formulas, which connect the roots of a quadratic equation to its coefficients.

Answer 3

To verify the relation between the roots and coefficients of a quadratic equation, we can start by considering a general quadratic equation in the form:

ax^2 + bx + c = 0

In your case, you have the quadratic equation x^2 + 9x + 18 = 0. So, a = 1, b = 9, and c = 18.

Now, the sum and product of the roots of a quadratic equation can be expressed in terms of its coefficients. Let's denote the roots of the equation as α and β.

1. The sum of the roots (α + β) is given by:

α + β = -b/a

In your case, this becomes:

α + β = -9/1 = -9

2. The product of the roots (α * β) is given by:

α * β = c/a

In your case, this becomes:

α * β = 18/1 = 18

So, the sum of the roots is -9, and the product of the roots is 18 for the quadratic equation x^2 + 9x + 18 = 0.

These relations between the roots (α and β) and the coefficients (a, b, and c) are known as Vieta's formulas. They hold for any quadratic equation of the form ax^2 + bx + c = 0. In your specific case, the values of α and β that satisfy these relations are the roots of the equation x^2 + 9x + 18 = 0.