Question

Help what is x^2-2x-24=0

I know you can use quadratic formula I just forgot how examples always help :)

Answer 1

`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`

Answer 2

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}}`