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Dvinal [7]
2 years ago
9

Use vieta's theorem to solve the problems.

Mathematics
1 answer:
Mnenie [13.5K]2 years ago
6 0

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

<h3>What is the Vieta Theorem?</h3>
  • 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 brainly.com/question/23509978

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