Answered

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

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

Verified Answer :

\(x^2-2x-24=0\\\\a=1;\ b=-2;\ c=-24\\\\\Delta=b^2-4ac\\\\\Delta=(-2)^2-4\cdot1\cdot(-24)=4+96=100\\\\x_1=\frac{-b-\sqrt\Delta}{2a};\ x_2=\frac{-b+\sqrt\Delta}{2a}\\\\x_1=\frac{2-\sqrt{100}}{2\cdot1}=\frac{2-10}{2}=\frac{-8}{2}=-4\\\\x_2=\frac{2+\sqrt{100}}{2\cdot1}=\frac{2+10}{2}=\frac{12}{2}=6\)

D3xt3R

There are another way to solve a quadratic equation we call, Sum and product.

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

\(x^2-2x-24=0\)

\(Sum=-\frac{b}{a}\)

\(Product=\frac{c}{a}\)

therefore

\(Sum=-\frac{(-2)}{1}=2\)

\(Product=\frac{-24}{1}=-24\)

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.

\(\boxed{\boxed{x_1=-4~~and~~x_2=6}}\)

Related Questions