# Let x1 and x2 be the roots of the quadratic equation x ^ -3x-7 = 0.

August 31, 2021 | education

| **Let x1 and x2 be the roots of the quadratic equation x ^ -3x-7 = 0. Make a quadratic equation, the roots of which are the numbers 1 / x1 and 1 / x2.**

The equation is given:

x ^ 2 – 3 * x – 7 = 0;

Let x1 and x2 be the roots of the equation. Let us apply Vieta’s theorem to them:

x1 + x2 = 3;

x1 * x2 = -7;

We now have a second equation of the form:

x ^ 2 + b * x + c = 0;

Its roots are 1 / x1 and 1 / x2.

By Vieta’s theorem, we get:

-b = 1 / x1 + 1 / x2 = (x1 + x2) / (x1 * x2);

c = 1 / x1 * 1 / x2 = 1 / (x1 * x2);

We substitute the expressions we know:

-b = 3 / (- 7) = -3/7;

c = – 1/7;

We get:

x ^ 2 – 3/7 * x – 1/7 = 0;

7 * x ^ 2 – 3 * x – 1 = 0.

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