Can anyone solve the following quadratic equation using the formula method...
Xsquared - 10x + 3 = 0
Please show working out so it is possible for me to follow and see where i am going wrong
Thanks
Let me try again...
$\displaystyle x^2 - 10x + 3 = 0$
It seems he's allowed to use the quadratic formula.
All quadratic equations are written in the format of $\displaystyle ax^2 + bx + c = 0$
That means that $\displaystyle a$ is the co-efficient of the$\displaystyle x^2$ ; $\displaystyle b$ is the co-efficient of $\displaystyle x$ ; and $\displaystyle c$ is the constant.
According to the quadratic formula:
$\displaystyle x = \frac{ -b \pm \sqrt{b^2 - 4ac} }{2a}$
All you have to do is substitute the corresponding co-efficients into the formula.
A standard quadratic equation is in the form
$\displaystyle ax^2 + bx + c = 0$
a, b and c being the coefficients.
The formula for the discriminant ($\displaystyle \Delta$) is
$\displaystyle \Delta = b^2 - 4ac$
If $\displaystyle \Delta > 0$, there are 2 different roots.
If $\displaystyle \Delta = 0$, there are 2 equivalent roots. ($\displaystyle x_1=x_2$)
If $\displaystyle \Delta < 0$, there are no real roots.
The roots are,
$\displaystyle x_1 = \frac{-b - \sqrt{\Delta}}{2a}$
$\displaystyle x_2 = \frac{-b + \sqrt{\Delta}}{2a}$
Now plug a, b and c in these formulas.
Let's say we write your equation this way.
$\displaystyle ax^2+bx+c=0$
where:
$\displaystyle a=1$
$\displaystyle b=-10$
$\displaystyle c=3$
now we have the coefficients we use in the equation.
$\displaystyle x_{1,2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$
Now you just put a,b and c into the equation and that's it.
There are usually 2 results for x.
Here's the full solution. Ask me about any step you do not understand/
$\displaystyle x = \frac{ +10 \pm \sqrt{100 - 4(1)(3)} }{2}$
$\displaystyle x = \frac{ +10 \pm \sqrt{100 - 12} }{2}$
$\displaystyle x = \frac{ +10 \pm \sqrt{88} }{2}$
BUT $\displaystyle \sqrt{88} = \sqrt{4} \times \sqrt{22}$
AND we know $\displaystyle \sqrt{4} = 2$
$\displaystyle x = \frac{ +10 \pm \sqrt{4} \cdot \sqrt{22} }{2}$
$\displaystyle x = \frac{ +10 \pm 2 \sqrt{22} }{2}$
Divide 10 by 2, and divide $\displaystyle 2 \sqrt{22}$ by 2
$\displaystyle x = +5 \pm \sqrt{22}$