Question

the root of which of the quadratic equations are 2 and -5​

Answer 1

A root x=a corresponds to a factor (x−a) .

So in our example, the quadratic must have factors

(x−2) and (x+8) .

The simplest quadratic would be the monic (having leading coefficient 1 ) one:

(x−2)(x+8)=x2+6x−16

So the quadratic equation you are looking for is:

x2+6x−16=0

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