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Algebra
Pregunta

A. Determine if the given equation is linear, quadratic, or neither.

1. $$4 x - 5 = 6$$

2. $$5 x + 7 = 3 ( x - 1 )$$

3. $$m ^ { 2 } - 5 m - 6 = 0$$

4. $$y ^ { 3 } + 6 y ^ { 2 } - 7 y = 8$$

5. $$\frac { 1 } { x - 8 } = x + 5$$

B. Write the following quadratic equations in standard form. Give the value of a, b, and $$c$$ .

1. $$x ^ { 2 } = 2 x - 1$$

2. $$10 m = 7 m ^ { 2 }$$

3. $$3 + 5 d = 4 d ^ { 2 }$$

$$4 \cdot 14 = 3 x - x ^ { 2 }$$

$$5 \cdot m ^ { 2 } - 6 m + 5 = 4 m ^ { 2 } - 8$$

Determine the solutions of each quadratic equation using the preseribed method.

A. Extracting Square Roots

1) $$4 x ^ { 2 } - 81 = 0$$

2) $$2 x ^ { 2 } - 32 = 66$$

B. Factoring

3) $$a ^ { 2 } - a - 2 = 0$$

4) $$x ^ { 2 } + x = 20$$

5) $$x ^ { 2 } - 22 x = - 120$$

I:

A. 1. linear;    2. linear;    3. quadratic;     4. neither;     5.  linear

B. 1. x^2-2x+1=0;     2. 7m^2-10m=0;     3.4d^2-5d-3=0;     4.x^2-3x+14=0;    5. 3m^2+6m-13=0

II:

A. 1. (2x+9)(2x-9)=0; x=-9/2, x=9/2;

2.$$x = 8 - \sqrt { 97 }$$ ,$$x = 8 + \sqrt { 97 }$$

B.

3.a^2-a-2=0  (a-2)(a+1)=0   a=2, a=-1

4. x^2+x-20=0  (x+5)(x-4)=0  x=-5,x=4

5.x^2-22x+120=0  (x-10)(x-12)  x=10,x=12

Solución
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