Question

Теорема виета. не решая уравнения 3x2-7x-11=0 найдите значения выражения x один во второй+ x два во второй. Срочно !!

Answer 1

Vieta's Theorem

Vieta's theorem provides a relationship between the roots of a polynomial and its coefficients. For a quadratic equation of the form \(ax^2 + bx + c = 0\), the sum of the roots is given by \(-\frac{b}{a}\) and the product of the roots is given by \(\frac{c}{a}\).

Applying Vieta's Theorem

For the quadratic equation \(3x^2 - 7x - 11 = 0\), we can use Vieta's theorem to find the sum and product of the roots without solving the equation.

Sum of the Roots (\(x_1 + x_2\)): According to Vieta's theorem, the sum of the roots of the quadratic equation \(ax^2 + bx + c = 0\) is given by \(-\frac{b}{a}\).

In this case, for the equation \(3x^2 - 7x - 11 = 0\), the sum of the roots is \(-\frac{-7}{3}\).

Product of the Roots (\(x_1 \cdot x_2\)): According to Vieta's theorem, the product of the roots of the quadratic equation \(ax^2 + bx + c = 0\) is given by \(\frac{c}{a}\).

In this case, for the equation \(3x^2 - 7x - 11 = 0\), the product of the roots is \(\frac{-11}{3}\).

Therefore, without solving the equation, we have found that the sum of the roots (\(x_1 + x_2\)) is \(\frac{7}{3}\) and the product of the roots (\(x_1 \cdot x_2\)) is \(\frac{-11}{3}\).