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What is the discriminant for the following equation?

\[ x^2 + 8x + 7 = 0 \]

A. \(\pm 6\)

B. 36

C. 6, -6

D. 36

E. -1, -7

F. 57

G. -1, -7

H. 57

Answer :

To find the discriminant of the quadratic equation [tex]\(x^2 + 8x + 7 = 0\)[/tex], we'll use the discriminant formula. The discriminant ([tex]\(D\)[/tex]) provides information about the nature of the roots of the quadratic equation and is given by:

[tex]\[
D = b^2 - 4ac
\][/tex]

In the equation [tex]\(x^2 + 8x + 7 = 0\)[/tex], we have:

- [tex]\(a = 1\)[/tex] (the coefficient of [tex]\(x^2\)[/tex]),
- [tex]\(b = 8\)[/tex] (the coefficient of [tex]\(x\)[/tex]),
- [tex]\(c = 7\)[/tex] (the constant term).

Now, substitute these values into the formula:

[tex]\[
D = (8)^2 - 4 \times 1 \times 7
\][/tex]

Calculate each part:

1. Calculate [tex]\(b^2\)[/tex]: [tex]\((8)^2 = 64\)[/tex].
2. Calculate [tex]\(4ac\)[/tex]: [tex]\(4 \times 1 \times 7 = 28\)[/tex].
3. Subtract the results: [tex]\(64 - 28 = 36\)[/tex].

So, the discriminant of the quadratic equation [tex]\(x^2 + 8x + 7 = 0\)[/tex] is [tex]\(36\)[/tex].

This means that the quadratic equation has two distinct real roots.

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