Question

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

Answer 1

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.

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

Answer 2

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