2.5.2 Sum of Roots and Product of Roots (Examples)

Example
The roots of 2 x 2 + 3 x 1 = 0   are α and β.  Find the values of
(a) ( α + 1 ) ( β + 1 )
(b) 1 α + 1 β
(c) α 2 β + α β 2
(d) α β + β α

[Clue: α 2 + β 2 = ( α + β ) 2 2 α β   ]





2.5.2a Forming New Quadratic Equation given a Quadratic Equation
Example
If the roots of x 2 3 x 7 = 0   are α  and β  , find the equation whose roots are α 2 β   and α β 2 .

Solution

Part 1 : Find SoR and PoR for the quadratic equation in the question




Part 2 : Form a new quadratic equation by finding SoR and PoR




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