# Thread: Finding the values of a and b

1. ## Finding the values of a and b

Hello everyone. This question is apparently unsolvable:

If $\displaystyle x = 3$ or $\displaystyle -4$ are the solutions of the equation $\displaystyle x^2+ax+b=0$, find the values of $\displaystyle a$ and $\displaystyle b$.

The keyword in this irksome question would be the word 'or'. So it denotes that that this involves quadratic formulas.

Can anyone give me a clue so that I may make a breakthrough in understanding this problem? Thank you so much!

2. The wording is a bit iffy, but they actually meant that the solutions for that equation is x = 3 AND x = -4.

3. Originally Posted by PythagorasNeophyte
This question is apparently unsolvable:

If $\displaystyle x = 3$ or $\displaystyle -4$ are the solutions of the equation $\displaystyle x^2+ax+b=0$, find the values of $\displaystyle a$ and $\displaystyle b$.
No this question IS solvable. And quite easily I might add.

We know the quadratic formula as having a $\displaystyle \pm$ which yields 2 answers.

Substituting in values from $\displaystyle x^2+ax+b=0$ into the quadratic formula we get:

$\displaystyle x=\dfrac{-a + \sqrt{a^2 - 4 \times 1 \times b}}{2}$ and $\displaystyle x=\dfrac{-a - \sqrt{a^2 - 4 \times 1 \times b}}{2}$

We know that the minus squareroot usually gives us the smaller answer of x. So then we just substitute in our x answers to get:

$\displaystyle 3=\dfrac{-a + \sqrt{a^2 - 4 \times b}}{2}$ and $\displaystyle -4=\dfrac{-a - \sqrt{a^2 - 4 \times b}}{2}$

Now solve for a and b using simultaneous equation.

4. Originally Posted by Educated
No this question IS solvable. And quite easily I might add.

We know the quadratic formula as having a $\displaystyle \pm$ which yields 2 answers.

Substituting in values from $\displaystyle x^2+ax+b=0$ into the quadratic formula we get:

$\displaystyle x=\dfrac{-a + \sqrt{a^2 - 4 \times 1 \times b}}{2}$ and $\displaystyle x=\dfrac{-a - \sqrt{a^2 - 4 \times 1 \times b}}{2}$

We know that the minus squareroot usually gives us the smaller answer of x. So then we just substitute in our x answers to get:

$\displaystyle 3=\dfrac{-a + \sqrt{a^2 - 4 \times b}}{2}$ and $\displaystyle -4=\dfrac{-a - \sqrt{a^2 - 4 \times b}}{2}$

Now solve for a and b using simultaneous equation.
That is a very methodical method, great for understanding concepts.

If you wish to know, a quicker way is to simply expand (x-3)(x+4) = 0.

5. I guess I overcomplicated things...

6. Another way: If x= 3 and x= -4 are roots of the equation $\displaystyle x^2+ ax+ b$, then [tex](x- 3)(x+ 4)= x^2+ ax+ b[tex]. Just multiply out the left side to find a and b.

I see that Gusbob already said that.