Question

Разность корней уравнения 2x²-3x+c=0 равна 2,5 Найдите с. помагите пожалуста решается с помощью теоремы Виета врорде

Answer 1

По теореме Виета:

ax^2+bx+c=0

x1+x2=-b\a

получается система

x1+x2=1,5

x1-x2=2,5

откуда мы узнаем 

x1=2

x2=-0,5

x1*x2=c\a

a=2

c=x1*x2*a=2*2*(-0,5)=-2

Ответ:-2

Answer 2

Solving the Quadratic Equation Using Vieta's Theorem

To find the value of the constant c in the quadratic equation 2x² - 3x + c = 0 given that the difference of the roots is 2.5, we can use Vieta's theorem. Vieta's theorem states that for a quadratic equation of the form ax² + bx + c = 0 with roots r1 and r2, the sum of the roots is -b/a and the product of the roots is c/a.

Applying Vieta's Theorem

The difference of the roots is given by the absolute value of the sum of the roots, which is equal to 2.5. Therefore, we have:

|r1 + r2| = 2.5

According to Vieta's theorem, the sum of the roots is -b/a and the product of the roots is c/a. We can use these relationships to solve for the constant c.

Calculating the Sum and Product of the Roots

The sum of the roots is given by -b/a and the product of the roots is c/a. We can use these relationships to solve for the constant c.

Let's denote the roots as r1 and r2. Then, according to Vieta's theorem:

1. Sum of the roots (r1 + r2) = -(-3)/2 2. Product of the roots (r1 * r2) = c/2

Using the Given Information

We are given that the difference of the roots is 2.5. This implies that the sum of the roots is either 2.5 or -2.5. Since the sum of the roots is negative, we have:

r1 + r2 = -2.5

Solving for the Constant c

Using the relationships from Vieta's theorem, we can solve for the constant c:

1. -b/a = -3/2 2. c/a = c/2

Given that r1 + r2 = -2.5, we can solve for the constant c using the sum and product of the roots.

Conclusion

By applying Vieta's theorem and using the given information about the difference of the roots, we can solve for the constant c in the quadratic equation 2x² - 3x + c = 0.