Mathematics

find the roots ?
x² + 7x + 12 =0

x²-8x +12=0


Answers

DestinyNicolle

4 years ago Comment

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]

yassautumn

4 years ago Comment

[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]