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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 :)

2 Answers

3 votes

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=(-b-\sqrt\Delta)/(2a);\ x_2=(-b+\sqrt\Delta)/(2a)\\\\x_1=(2-√(100))/(2\cdot1)=(2-10)/(2)=(-8)/(2)=-4\\\\x_2=(2+√(100))/(2\cdot1)=(2+10)/(2)=(12)/(2)=6
User SnekNOTSnake
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3 votes
There are another way to solve a quadratic equation we call, Sum and product.

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


x^2-2x-24=0


Sum=-(b)/(a)


Product=(c)/(a)

therefore


Sum=-((-2))/(1)=2


Product=(-24)/(1)=-24

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.


8+(-3)=5


8*(-3)=-24

Doesn't work.

Let's try now 4 and -6.


4+(-6)=-2


4*(-6)=-24

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

therefore

Let's try -4 and 6


6+(-4)=2


6*(-4)=-24


Sum=2

and


Product=-24

Them it works.


\boxed{\boxed{x_1=-4~~and~~x_2=6}}
User Victorp
by
7.5k points

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