Write a quadratic equation

Question

Write a quadratic equation having the given numbers as solutions 

 

-10 and -1

Answer 1

If "a" is a solution then x - a is a factor.

(x - (-10)) and (x - (-1)) are factors of the quadratic equation

(x + 10)(x + 1) = 0

x² + 11 x + 10 = 0

Answer 2

[x - (-10)][(x - (-1)] = 0

 

(x + 10)(x + 1) = 0

 

x² + 11 x  + 10 = 0 is the desired quadratic equation.

Answer 3

Both Arturo and Mark gave correct answers. Arturo gave a general solution for any value of A (A ≠ 0).

Mark gave the specific solution when A = 1.  The question asked for "a quadratic equation" and not "all quadratic equations" so Mark's answer may be closer to what your teacher is expecting.

Answer 4

Since the given numbers -10 and -1 are roots of f(x) = 0, a general form of f(x) would be

 

f(x) = A [x - (-10)] [x - (-1)] = A (x + 10) ( x + 1)

 

So f(x) = A (x + 10) (x + 1) where A is a constant, and A ≠ 0