# Solve

Find values for a, b and c, so that x = 3:

Later, a second formula will be provided if you haven’t already got it.

Hint: none of the four digits are outside the range minus 9 to plus 9.

Here’s that formula:

1. Mark in Mayenne
March 14, 2019 at 19:41

Looks like a quadratic. So (x-3) squared. a=1, b=6, c=9

2. Mark in Mayenne
March 14, 2019 at 19:42

Sorry b= -6

Not thinking straight

3. Mudplugger
March 14, 2019 at 20:10

That quadratic formula instantly rang a bell, a bell which had previously been un-rung for more than 50 years – I couldn’t be arsed then and can’t be arsed now.

As it didn’t seem to offer a certain channel to a Littlewoods jackpot or the chance of a first leg-over from the neighbouring girls’ school, it never seemed an important enough use of my precious teenage time.

4. Andy5759
March 14, 2019 at 20:50

Me brain ‘urts.

5. March 14, 2019 at 21:46

x = +3
a = +2
b = -4
c = -6

6. March 14, 2019 at 22:27

I agree with Mark in Mayenne. (x-3)*(x-3) = 0. This has the single solution x = +3.

James’s solution factorises as (x-3)*(2x+2) = 0. This has two different solutions for x; x = +3 and x = -1.

If one allows solutions with a second different value for x than +3, there are an infinite number of solutions.

Best regards

• March 15, 2019 at 03:41

Last para – but one doesn’t, as plus 3 was the given the question was based upon.

7. March 15, 2019 at 08:12

In addition to my earlier point (which James has clearly not understood), James’s solution ([a,b,c]=[+2,-4,-6]) has an arbitrary factor of 2 in it. Normal mathematical processing is to cancel out the common constant (2 in this case) giving [a,b,c]=[+1,-2,-3] as a solution.

Just to repeat, the correct solution for x = +3 is [a,b,c]=[+1,-6,+9]. Otherwise there are an infinite number of solutions: (x-3)(x-n)=0 where n can take any value.

Best regards

8. March 15, 2019 at 08:47

He actually did understand, hence the wording:

Find values for

… rather than the one correct answer.

However, there aren’t all that many when they must be whole numbers between minus 9 and plus 9.

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