perplexus.info :: Just Math : Quadratic Function Determination

Quadratic Function Determination (Posted on 2024-02-02)

Determine a quadratic function f(x) that satisfies this equation:
f(x)*f(x-1)= f(x^2)

See The Solution Submitted by K Sengupta

Rating: 5.0000 (2 votes)

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Using Wolfram Alpha

| Comment 2 of 4 |

Giving Wolfram Alpha

solve (x^2+x+c)*((x-1)^2+(x-1)+c) = x^4+x^2+c for c

finds c = 1

implying that

y = x^2 + x + 1 satisfies the condition given.

and

simplify (x^2+x+1)*((x-1)^2+(x-1)+1)

does give

x^4 + x^2 + 1

Posted by Charlie on 2024-02-02 11:07:30

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