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find the roots ? x² + 7x + 12 =0 x²-8x +12=0

MargaretteWalk409 Mathematics 2 7

find the roots ? x² + 7x + 12 =0 x²-8x +12=0

Posted by MargaretteWalk409 | Posted at Mar 26, 2000 | Categories: Mathematics

Answers

DestinyNicolle
DestinyNicolle

We have to remember one simple pattern [latex]Delta =b^2-4ac[/latex] 1. [latex]x^2+7x+12=0[/latex] in this case [latex]b=7[/latex] [latex]a=1[/latex] [latex]c=12[/latex] so: [latex]Delta =7^2-4*1*12[/latex] [latex]Delta =49-48[/latex] [latex]Delta =1[/latex] [latex]Delta >0[/latex] it means that there are 2 roots [latex]sqrt{Delta} =1[/latex] [latex]x_{1}=frac{-b+sqrt{Delta}}{2a}[/latex] [latex]x_{2}=frac{-b-sqrt{Delta}}{2a}[/latex] [latex]x_{1}=frac{-7+1}{2}[/latex] [latex]x_{1}=frac{-6}{2}[/latex] [latex]x_{1}=-3[/latex] [latex]x_{2}=frac{-7-1}{2}[/latex] [latex]x_{2}=frac{-8}{2}[/latex] [latex]x_{2}=-4[/latex] Roots are [latex]x_1=-4[/latex] and [latex]x_2=-3[/latex] 2. [latex]x^2-8x +12=0[/latex] in this case [latex]a=1[/latex] [latex]b=-8[/latex] [latex]c=12[/latex] [latex]Delta =(-8)^2-4*1*12[/latex] [latex]Delta =64-48[/latex] [latex]Delta =16[/latex] [latex]Delta >0[/latex] it means that there are 2 roots [latex]sqrt{Delta}=4[/latex] [latex]x_{1}=frac{-b+sqrt{Delta}}{2a}[/latex] [latex]x_{2}=frac{-b-sqrt{Delta}}{2a}[/latex] [latex]x_{1}=frac{8+4}{2}[/latex] [latex]x_{1}=frac{12}{2}[/latex] [latex]x_{1}=6[/latex] [latex]x_{2}=frac{8-4}{2}[/latex] [latex]x_{2}=frac{4}{2}[/latex] [latex]x_{2}=2[/latex] Roots:[latex]x_1=6[/latex] and [latex]x_2=4[/latex]

Mar 26, 2000 01:48
yassautumn
yassautumn

[latex]x^2 + 7x + 12 =0 x^2+4x+3x+12=0 x(x+4)+3(x+4)=0 (x+3)(x+4)=0 x=-3 vee x=-4\ x^2-8x+12=0 x^2-6x-2x+12=0 x(x-6)-2(x-6)=0 (x-2)(x-6)=0 x=2 vee x=6[/latex]

Mar 26, 2000 01:56

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