College Algebra

Question

Discuss under what conditions the following equation: a*x^2-4x+5=8 has two distinct real solutions? Carefully explain using calculations the values of a that would provide 2 real and distinct solutions.

 

Answer 1

Express the given equation as a quadratic equation in standard form, find the discriminant, and then determine the range of a that keeps the discriminant positive.

 

ax² - 4x + 5 = 8

 

ax² - 4x - 3 = 0

 

D = (-4)² - 4a(-3) > 0

 

16 + 12a > 0

 

a > -16/12

 

a > -4/3