14, -9 write a quadratic equation with these solutions. With 1 being there greatest common factor
a*x^2+bx+c=a*(x-x1)*(-x2)
Where is x1 and x2 roots of equation
In your case a=1 so:
x^2+bx+c=(x-x1)*(x-x2)=
(x-14)*[x-(-9)]=
(x-14)*(x+9)=
x*x-x*14+9*x-9*14=
x^2-14x+9x-126=
x^2-5x-126
To write a quadratic equation with given solutions, we can use the fact that the solutions of a quadratic equation can be found by factoring it. Given the solutions 14 and -9, we know that the factored form of the quadratic equation would be:
(x - 14)(x + 9) = 0
Now, we need to find the quadratic equation using this factored form. To do this, we can expand the equation:
(x - 14)(x + 9) = 0
x^2 + 9x - 14x - 126 = 0
x^2 - 5x - 126 = 0
So, the quadratic equation with the given solutions 14 and -9, and their greatest common factor being 1, is:
x^2 - 5x - 126 = 0