For what values of a does the quadratic inequality have no solution `2ax^2+(a+3)x+a-1>0`  

Expert Answers info

mathsworkmusic eNotes educator | Certified Educator

calendarEducator since 2012

write511 answers

starTop subjects are Math, Science, and Business

If the inequality `2ax^2 + (a+3)x + a -1 > 0` is to have no solution

this implies that the quadratic `2ax^2 + (a+3)x + a - 1` is strictly negative

ie that the quadratic `-2ax^2 - (a+3)x - a + 1` is strictly positive.

A quadratic is strictly positive when it has no real roots, that is, when it's determinant is negative.

The determinant is given by `B^2 - 4AC`  where `A ` is the coefficient of `x^2`, `B` is the coefficient of `x` and `C` is the zeroth order term.

Here, `A = -2a`, `B = -(a +3)`  and `C = 1 -a`

Therefore the determinant is given by `B^2 - 4AC = (a+3)^2 - 4(-2a)(1-a)`

This is negative if `a^2 + 6a + 9 - 4(-2a + 2a^2) =...

(The entire section contains 2 answers and 337 words.)

Unlock This Answer Now


check Approved by eNotes Editorial

sciencesolve eNotes educator | Certified Educator

calendarEducator since 2011

write5,349 answers

starTop subjects are Math, Science, and Business

check Approved by eNotes Editorial