Question

Один из корней квадратного уравнения 4x^2-15x+c=0 в 4 раза больше второго. Найдите С.

Answer 1

D=225-16c<br />x1=(15+√(225-16c))/8<br />x2=(15-√(225-16c))/8<br />15+√(225-16c)=4(15-√(225-16c))<br />-45=-5√(225-16c)<br />9=√(225-16c)<br />81=225-16c<br />c=144/16=9

Answer 2

Finding the Value of C in a Quadratic Equation

To find the value of C in the quadratic equation 4x^2 - 15x + c = 0, given that one of the roots is four times larger than the other, we can use the properties of quadratic equations.

Let's assume the roots of the equation are x1 and x2, with x1 being four times larger than x2.

According to the properties of quadratic equations, the sum of the roots (x1 + x2) is equal to -b/a, and the product of the roots (x1 * x2) is equal to c/a, where a, b, and c are the coefficients of the quadratic equation.

In this case, the coefficient of x^2 is 4, the coefficient of x is -15, and the coefficient of the constant term is c.

Using the given information, we can write the following equations:

x1 + x2 = -(-15)/4 x1 * x2 = c/4

Since x1 is four times larger than x2, we can substitute x2 with x1/4 in the above equations:

x1 + x1/4 = -(-15)/4 x1 * (x1/4) = c/4

Simplifying the equations:

(5/4)x1 = 15/4 (x1^2)/4 = c/4

Multiplying both sides of the first equation by 4/5, we get:

x1 = 3

Substituting x1 = 3 into the second equation, we get:

(3^2)/4 = c/4 9/4 = c/4

Multiplying both sides of the equation by 4, we get:

9 = c

Therefore, the value of C in the quadratic equation 4x^2 - 15x + c = 0, where one of the roots is four times larger than the other, is 9.