Question

Dimitri and Jillian were trying to solve the equation:(x+1)(x+3)=12(x+1)(x+3)=12(x+1)(x+3)=12left parenthesis, x, plus, 1, right parenthesis, left parenthesis, x, plus, 3, right parenthesis, equals, 12Dimitri said, "The left-hand side is factored, so I'll use the zero product property."Jillian said, "I'll multiply (x+1)(x+3)(x+1)(x+3)(x+1)(x+3)left parenthesis, x, plus, 1, right parenthesis, left parenthesis, x, plus, 3, right parenthesis and rewrite the equation as x2+4x+3=12x^2+4x+3=12x2+4x+3=12x, squared, plus, 4, x, plus, 3, equals, 12. Then I'll solve using the quadratic formula with a=1a=1a=1a, equals, 1, b=4b=4b=4b, equals, 4, and c=3c=3c=3c, equals, 3.Whose solution strategy would work?Choose 1 answer:Choose 1 answer:(Choice A)AOnly Dimitri's(Choice B)BOnly Jillian's(Choice C)CBoth(Choice D)DNeither

Answer 1

d

Explanation:

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Answer 2

D. Neither

Explanation:

The equation that Dimitri and Jillian were trying to solve is expressed as

(x+1)(x+3) = 12. They are both solving this equation to get the value of x.

Based on the their suggestion, Jillian strategy would have been the best and the only one that will work for us in solving the equation but he didn't take cognizance of 12 when using the formula in his second step hence None of them are correct. The following steps should have been taken;

Step 1: Multiply out the expression (x+1)(x+3)

= (x+1)(x+3)

= x(x)+ 3x+x+1(3)

= x² + 3x + x + 3

= x² + 4x + 3

He got x² + 4x + 3 on expansion

Step 2: He should have rewrote the equation as shown;

x² + 4x + 3 = 12

x² + 4x + 3 -12 = 0

x² + 4x -9 = 0

Step 3: He used the quadratic formula to factorize the expression x² + 4x + 3 where a = 1, b = 4 anad c = -9

x = (-b±√b²-4ac)/2a

x = (-4±√(4)²-4(1)(-9))/2(1)

x = -4±√16+36/2

x = (-4±2√13)/2

x = (-4+2√13)/2 or (-4-2√13)/2

x = -2+√13 or -2-√13

Hence Neither of them is correct. Jillian is almost correct but he should have equated the equation to zero by taking 12 into consideration before factorizing.