Knowing A and the discriminant, how to find

poznateqojh

poznateqojh

Answered question

2022-04-13

Knowing A and the discriminant, how to find B and C?
On a Quadratic equation of the form ax2+bx+c, I am given the discriminant Δ=b24ac and A.
To find B and C, I tried to solve it through x1 and x2...:
- x1=bΔa
- x2=b+Δa
...using those properties:
- x1+x2=ba
- x1×x2=ca
Without any success...
So, is it possible to retrieve B and C?
Two additional properties:
- the discriminant is always positive
- B is always negative

Answer & Explanation

cadhail6n1t

cadhail6n1t

Beginner2022-04-14Added 14 answers

Step 1
Δ=B24AC (1)
with 2 unknowns B and C: there is a fundamental indeterminacy.
A counterexample among many: If A=14 and Δ=16, (1) becomes:
16=B2C
which is possible for (B=4, C=0),(B=5, C=9),(B=6, C=20), etc. (I have taken into account the constraint on B to be negative).
Step 2
Otherwise said,
14x24x=0,   14x25x+9=0,   14x26x+25=0
have all the same A and the same Δ without having the same B and the same C.

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