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Mechanical Integration

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Janusz Asked

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2
For $y = ax + b$, if you can use the given conditions and write $b$ in terms of $a$, then for any value of $a$ there will be a linear function with this property.

For the second part use the formula relating the sum of the roots and the coefficients and then work systematically to consider all cases.