Question

X^2+32+48 теорема Виета

Answer 1

Ответ:

Р

Объяснение:

x^2+bx+32=0 при х=4

4^2+4b+32=0

4b=-48

b=-12

x^2-12x+32=0

D=b^2-4ac

D=144-128=16

x1=(12-4)/2=8/2=4

x2=(12+4)/2=16/2=8

Ответ:b=-12 x2=8

Answer 2

Quadratic Equation and Vieta's Theorem

The quadratic equation is typically represented as ax^2 + bx + c = 0, where a, b, and c are constants and x is the variable. Vieta's theorem provides a relationship between the roots of a quadratic equation and its coefficients.

Vieta's theorem states that for a quadratic equation ax^2 + bx + c = 0 with roots r1 and r2, the following relationships hold: - r1 + r2 = -b/a - r1 * r2 = c/a

Let's use Vieta's theorem to find the sum and product of the roots for the quadratic equation x^2 + 32x + 48 = 0.

The sum of the roots (r1 + r2) is given by -b/a, and the product of the roots (r1 * r2) is given by c/a.

Using the coefficients from the given quadratic equation: - a = 1 - b = 32 - c = 48

We can now apply Vieta's theorem to find the sum and product of the roots.

Sum of the roots: The sum of the roots is given by -b/a. Substituting the values: - Sum of the roots = -32/1 = -32

Product of the roots: The product of the roots is given by c/a. Substituting the values: - Product of the roots = 48/1 = 48

So, according to Vieta's theorem, for the quadratic equation x^2 + 32x + 48 = 0: - Sum of the roots = -32 - Product of the roots = 48

This demonstrates the application of Vieta's theorem to find the relationship between the roots and coefficients of a quadratic equation.