Question

Use vieta's theorem to solve the problems.
the difference of the two solutions of x^2 - 17x + c = 0 is 1. find c.

Answer 1

Using Vieta's Theorem, it is found that c = 72.

What is the Vieta Theorem?

• Suppose we have a quadratic equation, in the following format:

$y = ax^2 + bx + c$

• The roots are p and q.

The Theorem states that:

$p + q = -\frac{b}{a}$

$pq = \frac{c}{a}$

In this problem, the polynomial is:

$x^2 - 17x + c$

Hence the coefficients are $a = 1, b = -17$.

Since the difference of the solutions is 1, we have that:

$p - q = 1$

$p = 1 + q$

Then, from the first equation of the Theorem:

$p + q = -\frac{b}{a}$

$1 + q + q = 17$

$2q = 16$

$q = 8$

$p = 1 + q = 9$

Now, from the second equation:

$pq = \frac{c}{a}$

$72 = c$

$c = 72$

To learn more about Vieta's Theorem, you can take a look at https://brainly.com/question/23509978