Question

The difference of the two solutions of x2−17x+c=0 is 1. Find the solutions.

Answer 1

To find the solutions of the equation x² - 17x + c = 0, where the difference of the two solutions is 1, we can use the quadratic formula.

Step-by-step explanation:

To find the solutions of the equation x² - 17x + c = 0, where the difference of the two solutions is 1, we can use the quadratic formula. The quadratic formula states that for an equation of the form ax² + bx + c = 0, the solutions are given by:

x = (-b ± √(b² - 4ac)) / (2a)

In this case, we have a = 1, b = -17, and c = c. We can substitute these values into the formula and solve for x.

Answer 2

In a quadratic equation, the additive inverse of the quotient of the second term and the first term is the sum of the roots. Using this concept,
x1 + x2 = -(-17/1)
x1 - x2 = 1
The value of x1 is equal to 9 and the value of x2 is 8. Therefore, the roots are 9 and 8.