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Question

Solve the following quadratic equation by factorization :
Solve for x:x1x2+x3x4=313,x2,4

A
5, 52
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B
5, 52
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C
5, 52
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D
5, 52
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Solution

The correct option is C 5, 52
x1x2+x3x4=313

(x1)(x4)+(x3)(x2)(x2)(x4)=103

x24xx+4+x22x3x+6x24x2x+8=103

2x210x+10x26x+8=103

2(x25x+5)x26x+8=103

x25x+5x26x+8=53

3x215x+15=5x230x+40
2x215x+25=0
2x2105x+25=0
2x(x5)5(x5)=0
(x5)(2x5)=0
x5=0 and 2x5=0
x=5 and x=52


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