Solve 3x2 + x - 10 = 0. Round solutions to the nearest hundredth. (5 points) a x ≈ −5 and x ≈ 2 b No real solutions c x ≈ −2 and x ≈ 1.67 d x ≈ −1.67 and x ≈ 2

c) x ≈ −2 and x ≈ 1.67

Step-by-step explanation:

Solve 3x²+ x - 10 = 0.

We solve using Almighty formula

-b ± √b² - 4ac/2a for equation: ax² + bx + c

where a = 3, b = 1, c = -10

Hence

-1 ± √1² - 4 × 3 × -10/2 × 3

-1 ± √1 - (-120)/6

-1 ± √1 + 121/6

-1 ± √121/6

-1 ± 11/6

Hence:

-1 - 11/6

-12/6 = -2

-1 + 11/6

= 10/6

= 1.67

Therefore, x = -2, x = 1.67

Option c) x ≈ −2 and x ≈ 1.67 is the correct answer

geometric series converge the common ratio r has magnitude less than one.

which is equivalent to

for the example we need

|2-x| < 1

-1 < 2-x   and 2-x < 1

x < 3 and x > 1

we can write that

answer: 1 < x < 3

1a. common ratio r=250/25=10 > 1     diverges

1b.   r=50/100=1/2 converges

when these converge they converge to

where a is the first term.

answer: 200

1c. r=-1   so it's not the case that |r| < 1.     diverges

2a. x is the common ratio so we converge when |x|< 1

2b.   r=-10x / -2 = 5x.

we converge when

|5x| < 1

|x| < 1/5

2c.   r=3-2x

-1 < 3-2x and 3-2x < 1

-4 < -2x and 2 < 2x

x < 2 and 1 < x

1 < x < 2

2d. [/tex] r=-48x^3/12 = 4x^3[/tex]

|4x^3| < 1

|x^3| < \frac 1 4

|x| < 4^{-1/3}

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