Question

A quadratic equation ax^2+bx+c=0 has -11 and 4 as solutions. Find the values of b and c if the value of a is 1 (hint, use zero factor property in reverse)
The quadratic equation has a=1, b= ____, and c = ____

Answer 1

Answer:

b = 7, c = -44

Step-by-step explanation:

If the quadratic equation has the solutions -11 and 4, the two factors are:

$(x+11)(x-4)=0$

Since when we use the zero factor property we get

x+11=0 ⇒ x= -11

x-4=0 ⇒  x=4

Thus, we have used the zero factor property in reverse to find the factorization of the quadratic equation.

Now we develop the multiplications between parenthesis:

$(x+11)(x-4)=0\\x^2-4x+11x-44=0\\x^2+7x-44=0$

So b is the number that accompanies the x: b = 7

and c is the independent number: c = -44