Read Finding the common root by subtracting two quadratics with a shared x^2 coeffi
This SEHSS pattern tests Subtracting ax²+8bx+7c=0 and ax²+2bx+c=0 to isolate the common root as -c/b, then substituting to derive the condition b²=ac (Geometric Progression). Read the condition carefully, then use the method below before you solve.
Mathematics questions are solved by expressing every restriction precisely before transforming or counting.
Find the tested idea
Translate the wording into variables, a diagram or a counting condition before manipulating expressions.
Build the solution
Use one exact relationship at a time. Organise cases so they are complete and non-overlapping, then test every candidate against the original condition.
Verify before choosing
Return to the exact wording and check that the conclusion satisfies every stated condition, unit and definition.
OlympIQ exam lens
- ✓State variables and restrictions.
- ✓Apply one justified step at a time.
- ✓Check every answer in the original problem.
A transformed equation or counted case is valid only if it preserves every original restriction.
Ready to try the pattern?
100% coverage across the linked question.
Practise the linked question