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May 6, 2016
Posted by **Unknown** on Monday, August 20, 2012 at 8:07pm.

Quadratic Equations ;

1. 4y^4+9=13y^2

2. x-3x 1/2+2=0

3. (x-5)^2+2(x-5)-35=0

4. (x-2)^2-3(x-2)+2=0

5. 2(x^2-5) - 13(x^2-5)+20=0

6. 2x 2/3 + 5 1/3=12

7.6x 2/3 -5x 1/3-6=0

8.x^-2 + 4x^-1=12

9.x^4-8x^2+7=0

10.x^4-2x^2-35=0

- Algebra. -
**Henry**, Wednesday, August 22, 2012 at 7:02pm1. 4y^4 + 9 = 13y^2.

4y^4 - 13y^2 + 9 = 0

Uwse the AC method of factoring.

A*C = 4*9 = 36 = (-1)*(-36) = (-4)*(-9).

Use the pair of factors whose sum = -13.

4y^4 + (-4y^2-9y^2) +9 = 0

Arrange the 4 terms to form 2 factorable pairs:

(4y^4-4y^2) - (9y^2-9) = 0

4y^2(y^2-1) - 9(y^2-1) = 0

(y^2-1)(4y^2-9) = 0

(y+1)(y-1)(2y+3)(2y-3) = 0.

y+1 = 0, Y = -1.

y-1 = 0, Y = 1.

2y+3 = 0, Y = -3/2.

2y-3 = 0, Y = 3/2.

Solution set: Y = -1,1,-3/2, and 3/2.

2.

3. (x-5)^2 + 2(x-5)-35 = 0.

x^2-10x+25 +2x-10-35 = 0

x^2-8x-20 = 0

(x+2)(x-10) = 0

x+2 = 0, X = -2.

x-10 = 0, X = 10.

Solution set: X = -2, and 10.

4. Same procedure as #3.

5. 2(x^2-5) - 13(x^2-5) +20 = 0.

(x^2-5)(2-13) + 20 = 0

-11x^2 + 55 + 20 = 0

-11x^2 + 75 = 0

2x^2 -10 -13x^2 + 65 + 20 = 0

-11x^2 + 75 = 0

-11x^2 = -75

x^2 = 6.818

X = 2.61, and-2.61.

8. x^-2 + 4x^-1 = 12.

1/x^2 + 4/x = 12

1 + 4x = 12x^2

12x^2 - 4x - 1 = 0.

A*C = 12*(-1) = -12 = 1(-12) = 2(-6).

Select the pair of factors whose sum=-4:

12x^2 + (2x-6x) -1 = 0

Arrange the 4 terms into 2 factorable

pairs:

(12x^2-6x) + (2x-1) = 0

6x(2x-1) + 1(2x-1) = 0

(2x-1)(6x+1) = 0.

2x-1 = 0, X = 1/2.

6x+1 = 0, X = -1/6.

Solution set: X = -1/6, and 1/2.

9. x^4 - 8x^2 + 7 = 0.

(x^2-1)(x^2-7) = 0

(x+1)(x-1)(x^2-7) = 0.

x+1 = 0, X = -1.

x-1 = 0, X = 1.

x^2-7 = 0, x^2 = 7, X = 2.65, and -2.65.

Solution set: X=-1,1,2.65, and -2.65.

10. Same procedure as #9.