Solving quadratics: the Square Root Principle

Solving quadratics: the Square Root Principle

: S C I T A R T D O A U RO Q E

R G N UA I LV SQ LE SO E CIP TH IN 3 PR R T P A

TO APPLY THE SQUARE ROOT PRINCIPLE THE QUADRATIC EQUATION MUST BE WRITTEN AS A A = (a + b)2 TO SOLVE USING THE SQUARE ROOT PRINCIPLE Must have perfect square variable expression on one side and constant on the other ;

notethe constant doesnt have to be a perfect square, just the variable expression must be perfect Examples: x2 = 16 (x 4)2 = 9 (2x 1)2 = 5

Click icon to add picture Circle the perfect squares X2 = 4 8 16n2 + 2n = 4 36d2 = 1 a2 =

APPLYING THE SQUARE ROOT PRINCIPLE RATIONAL ROOTS x2 = 16 x=4 APPLYING THE SQUARE ROOT PRINCIPLE IRRATIONAL ROOTS a2 = 8

= Graph can be deceiving!! Use the CALC functions to verify. Answer is very close to 3 () as () should be! BUT IT IS NOT 3!!! Because the graph is symmetrical to the yaxis, the other irrational root is approximately -2.828427. Verify with your calculator that is APPLYING THE SQUARE ROOT PRINCIPLE

(m + 3)2 = 10 m+3= m = -3 Verify with calculator APPLY THE SQUARE ROOT PRINCIPLE 36d2 = 1 1)2 = 3

(2k - IN QUADRATIC EQUATIONS Irrational roots ALWAYS come in CONJUGATE PAIRS If you have one irrational root, then you will have another one!! WHAT ARE THE SOLUTIONS TO THE

EQUATION? = 48 HINT: Isolate the x2, then apply the square

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