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help what is x^2-2x-24=0
I know you can use quadratic formula I just forgot how examples always help :)



Answer :

[tex]x^2-2x-24=0\\\\a=1;\ b=-2;\ c=-24\\\\\Delta=b^2-4ac\\\\\Delta=(-2)^2-4\cdot1\cdot(-24)=4+96=100\\\\x_1=\frac{-b-\sqrt\Delta}{2a};\ x_2=\frac{-b+\sqrt\Delta}{2a}\\\\x_1=\frac{2-\sqrt{100}}{2\cdot1}=\frac{2-10}{2}=\frac{-8}{2}=-4\\\\x_2=\frac{2+\sqrt{100}}{2\cdot1}=\frac{2+10}{2}=\frac{12}{2}=6[/tex]
D3xt3R
There are another way to solve a quadratic equation we call, Sum and product.

Let's see how we can do this...

[tex]x^2-2x-24=0[/tex]

[tex]Sum=-\frac{b}{a}[/tex]

[tex]Product=\frac{c}{a}[/tex]

therefore

[tex]Sum=-\frac{(-2)}{1}=2[/tex]

[tex]Product=\frac{-24}{1}=-24[/tex]

now we have to pick up 2 numbers that the sum should be 2 and the product should be -24, we just have to think a little.

Let's try -3 and 8, for example.

[tex]8+(-3)=5[/tex]

[tex]8*(-3)=-24[/tex]

Doesn't work.

Let's try now 4 and -6.

[tex]4+(-6)=-2[/tex]

[tex]4*(-6)=-24[/tex]

Can you see here, that we have to change the signal?!

therefore

Let's try -4 and 6

[tex]6+(-4)=2[/tex]

[tex]6*(-4)=-24[/tex]

[tex]Sum=2[/tex]

and

[tex]Product=-24[/tex]

Them it works.

[tex]\boxed{\boxed{x_1=-4~~and~~x_2=6}}[/tex]

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