Finding out the quadratic equation using Vieta?

Question

So I have the solutions to a quadratic equation:

$x_1=\frac{-3}{2}$

$x_2=\frac{1}{4}$

$x^2+px+q=0$ (Just telling you as I've seen many people using other letters for the variables)

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I tried solving it using

$-(x_1+x_2)=p$ and $x_1x_2=q$

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and getting p and q and then just inserting them into the formula but if I then try to solve this equation it does not return the results I have here. Can anyone tell me what I'm doing wrong?

Answer 1

$$-(x_1+x_2)=\frac{5}{4}$$

$$x_1x_2=\frac{-3}{8}$$

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Plugging gives:

$$x^2+\frac{5}{4}x-\frac{3}{8}=0$$

Multiplying each term by 8, gives:

$$8x^2+10x-3=0$$

$$(4x-1)(2x+3)=0$$

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Now let's solve this,

The solutions as expected are:

$$x_1=\frac{1}{4}$$ $$x_2=\frac{-3}{2}$$

So you do get the correct answers!

I think your not getting it because of some careless mistake, or because you didn't repeat doing it over again (to check for an arithmetic error)

Answer 2

since $x_1 and x_2$ are the two solutions of equation .So they must satisfy it .Just plug them in ur equation and u will get two equations in $p$ and $q$ . Solve them by elimination or any of your favourite methods you learned in high school