SOLUTION: Determine the type (real or complex) and number of the solutions of each of the following equations. Justify your answer. square root 2x^2-4x-7 square root 2=0 not sure how t

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Determine the type (real or complex) and number of the solutions of each of the following equations. Justify your answer. square root 2x^2-4x-7 square root 2=0 not sure how t      Log On


   

Question 194142: Determine the type (real or complex) and number of the solutions of each of the following equations. Justify your answer.
square root 2x^2-4x-7 square root 2=0
not sure how to make the square root symbol. Thank you
Found 3 solutions by jim_thompson5910, RAY100, solver91311:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
From sqrt%282%29x%5E2-4x-7%2Asqrt%282%29 we can see that a=sqrt%282%29, b=-4, and c=-7%2Asqrt%282%29


D=b%5E2-4ac Start with the discriminant formula.


D=%28-4%29%5E2-4%28sqrt%282%29%29%28-7%2Asqrt%282%29%29 Plug in a=sqrt%282%29, b=-4, and c=-7%2Asqrt%282%29


D=16-4%28sqrt%282%29%29%28-7%2Asqrt%282%29%29 Square -4 to get 16


D=16--56 Multiply 4%28sqrt%282%29%29%28-7%2Asqrt%282%29%29 to get


D=16%2B56 Rewrite D=16--56 as D=16%2B56


D=72 Add 16 to 56 to get 72


Since the discriminant is greater than zero, this means that there are two real solutions.

Answer by RAY100(1637) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt(2) x^2 -4x -7sqrt2 =0
,
discriminant
,
sq rt (b^2 -4 a c),,,where a=sqrt2,,,b=(-4),,,,c=(-7sqrt2)
,
subst
,
sq rt ((-4)^2 -4 (sqrt2) (-7sqrt2) )
sq rt( 16 +2*4*7)
sqrt 72
8.48
,
since discr is >0, two answers
remember if less than 0,,,,no solution,,,(complex no )
and if = 0,,,, only one solution
,
plugging this into the full quadratic eqn we find,
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x= ( 4+/- 8.48 ) /2.828,
,
or x = 4.415, or x= -1.586
,
check by subst back into origonal, both ok

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!




So:







Discriminant:



Plug in the values and calculate.

One point of intersection (the x-axis is tangent to the curve at the vertex)

Two points of intersection, i.e. two real number roots.

No points of intersection, i.e. the roots are a conjugate pair of complex numbers.

By the way, just use sqrt([argument]) to render square root. So your equation should have been written

2x^2 - 4x - 7*sqrt(2) = 0.

John