SOLUTION: Determine the number of solutions and classify the type of solutions for each of the following equations. Justify your answer. x2 � 4x

SOLUTION: Determine the number of solutions and classify the type of solutions for each of the following equations. Justify your answer. x2 � 4x - 77 = 0

Question 194177: Determine the number of solutions and classify the type of solutions for each of the following equations. Justify your answer.
x2 � 4x - 77 = 0
Answer by RAY100(1637) (Show Source): You can put this solution on YOUR website!
x^2 -4x -77
,
use discriminate to check number of answers
remember, D less than 0,,,,,no solutions
,,,,,,,,,,,,,,,,,,,D =0, one solution
,,,,,,,,,,,,,,,,,,,D >0, two solutions
,
a=1,,b=(-4),,c=(-77),,,, D= sqrt ( b^2 - 4 * a * c )
,
D = sq rt ( (-4)^2 - 4 (1) ( -77) ) = sqrt ( 16 + 308 ) =sqrt ( 324) = 18
therefore, D >0,,,and two solutions
,
completing quadratic eqn ( or factoring original )
,
x = ( 4 +/- 18 )/2 = 11, and -7
checking by substituting both in original eqn ,,both = 0,,,ok
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