# A level maths help

Find the set of values of a for which the equation

ax2 + 3x+ 2 = 0

has two distinct roots.
(edited 7 months ago)
I did ax2 +3x +2 =0
b2 -4ac=0
so (3x)2 - 4 x a x2
9x2 - 8a =0
but i don't know what to do next
Original post by user987789
I did ax2 +3x +2 =0
b2 -4ac=0
so (3x)2 - 4 x a x2
9x2 - 8a =0
but i don't know what to do next

Couple of things:

* The discriminant doesn't include any "x" or "x^2" terms.

* Discriminant = 0 is the condition for two equal roots, not two distinct roots.
For distinct roots, b2 -4ac > 0
Use b=3 the coefficient not 3x.
Original post by old_engineer
Couple of things:

* The discriminant doesn't include any "x" or "x^2" terms.

* Discriminant = 0 is the condition for two equal roots, not two distinct roots.

Okay so,

ax2 +3x +2 >0
b^2 -4ac> 0
3^2 - 4 x a x2>0
9 -8a >0
9 - 8 > a
1 > a

is that correct?
Original post by user987789
Okay so,

ax2 +3x +2 >0
b^2 -4ac> 0
3^2 - 4 x a x2>0
9 -8a >0
9 - 8 > a
1 > a

is that correct?

9 - 8a > 0 is correct, but you've gone wrong after that. Try adding 8a to both sides.
Original post by old_engineer
9 - 8a > 0 is correct, but you've gone wrong after that. Try adding 8a to both sides.

9 -8a >0
9> 8a
9/8 > a
is that right?
Original post by user987789
9 -8a >0
9> 8a
9/8 > a
is that right?

Yes that's correct, although you'd normally present the answer as a < 9/8
Original post by old_engineer
Yes that's correct, although you'd normally present the answer as a < 9/8

Thank you so much, so I don't need two solutions for these types of questions?
Original post by user987789
Thank you so much, so I don't need two solutions for these types of questions?

There’s only one range for this question. But you need to consider other questions on a case by case basis.
Original post by user987789
Thank you so much, so I don't need two solutions for these types of questions?

One thing you need to consider seperately is a=0, as its not a quadratic in that case so the discriminant analysis doesnt apply.