Explain how to solve the inequality ax^2 +by+c greater than 0 with a not equal to 0 using only the sign of a and the x-intercepts of f(x)=ax^2+bx+c.

Question

critical thinking/ discussion/ writing

Answer 1

ax² + bx + c > 0

 

 

Let the following be

 

x₁ = (-b - √(b² - 4ac)) / 2a

x₂ = (-b + √(b² - 4ac)) / 2a

 

Note that x₁ is the least x-intercept because the value is negative.  x₂ is the greater x-intercept because the value is positive.

 

This is when the inequality is zero.  Parabola is on the x-axis.

 

If a is negative, the parabola opens downward. Then the inequality is greater than zero (above the x-axis) when

 

x₁ < x < x₂

 

 

If a is positive, the parabola opens upward.  Then the inequality is greater than zero when

 

x < x₁        or            x > x₂