Find the exact solution to 6x^2+1= -8x by using the Quadratic Formula.

Answer: -4 +/- sqrt 10

2)Which describes the number and type of roots of the equation x^2-625=0?

Answer: 2 real roots

3)If g(x)=3x-8, find g[g(-4)]

Answer: -20

first two are correct.

for the third:
g(-4) = -12-8 = -20
then g(-20) = -60-8 = -68

To find the exact solution to the equation 6x^2 + 1 = -8x, we can use the Quadratic Formula.

The Quadratic Formula states that for an equation in the form ax^2 + bx + c = 0, the solutions are given by:

x = (-b ± sqrt(b^2 - 4ac)) / (2a)

In this case, a = 6, b = -8, and c = 1. Plugging these values into the formula, we get:

x = (-(-8) ± sqrt((-8)^2 - 4 * 6 * 1)) / (2 * 6)
= (8 ± sqrt(64 - 24)) / 12
= (8 ± sqrt(40)) / 12
= (8 ± sqrt(4 * 10)) / 12
= (8 ± 2sqrt(10)) / 12
= 2(4 ± sqrt(10)) / 12

Simplifying further, we get:

x = (4 ± sqrt(10)) / 6

Therefore, the exact solution to the equation 6x^2 + 1 = -8x is x = (4 ± sqrt(10)) / 6.

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For the equation x^2 - 625 = 0, we can determine the number and type of roots by looking at the discriminant of the Quadratic Formula.

The discriminant is given by b^2 - 4ac. If the discriminant is greater than zero, the equation has two real roots. If it is equal to zero, the equation has one real root (a double root). And if it is less than zero, the equation has two complex roots (conjugate pairs).

In this case, a = 1, b = 0, and c = -625. Plugging these values into the discriminant, we get:

Discriminant = b^2 - 4ac
= 0^2 - 4 * 1 * (-625)
= 2500

Since the discriminant is greater than zero (2500 > 0), the equation x^2 - 625 = 0 has two real roots.

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To find g[g(-4)] for the function g(x) = 3x - 8:

First, substitute -4 into g(x): g(-4) = 3(-4) - 8
= -12 - 8
= -20

Now, substitute -20 into g(x): g[g(-4)] = g[-20] = 3(-20) - 8
= -60 - 8
= -68

Therefore, g[g(-4)] = -68.