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Maxima and minima

a>0 min

a<0 max

x=-b/2a

val = (4ac-b^2)/4a

complete squares

Sum of roots(-b/a)

Product oof roots(c/a)

Nature of roots

Sign of roots

Roots reciprocal of given pair of roots then invert a and c

Adding of value to roots

Subtracting

Multiplication

Division

Complete squares to arrive at maxima minima value

To find range etc equate to k and solve with real solution condition

If question requires relationship between coefficients, express coefficients as sum and product of roots and then look for relation connecting them

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