Question

help write an quadratic equation having the given numbers as solutions
-10 and -1

Answer 1

if a,b are the solutions to a quadratic
then the quadratic is given by
(x-a)(x-b)=0

Answer 2

thus here it must be the product of (x+1)(x+10)=0

Answer 3

This is saying if x=-10 then \[ax^2+bx+c= 0\] and the same thing for -1 we know we can factor this into \[(x \pm d )(x \pm e)\] so if either of those are zero then the whole thing is zero and we call those numbers roots. They gave of us roots so we get \[(x+10)(x+1)=x^2+11x+10\] you can check this by plugging in the numbers given

Answer 4

alternative :
x^2 - (a+b)x + ab = 0 (with a, b are its solution)
here given a=-10 and b=-1 (or reverse)
x^2 - (-10-1)x + (-10)(-1) = 0
x^2 + 11x + 10 = 0