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The function g(x) = 4x^2 - 4x + m has exactly one zero. What is the value of m?

For what values of k does the equation 3x^2 + 4x + k = 0 have no real roots? One real root? Two real roots?

 Jun 9, 2019
 #1
avatar+101871 
+3

4x^2 - 4x + m

 

If this has one zero.....then the discriminant  = 0    ....so....

 

(-4)^2 - 4(4)m  = 0

 

16 - 16m  = 0

 

16 = 16m     divide both sides by 16

 

1  = m

 

 

cool cool cool

 Jun 9, 2019
 #2
avatar+101871 
+2

For what values of k does the equation 3x^2 + 4x + k = 0 have no real roots? One real root? Two real roots?

 

No real roots  if the discriminant is <  0   ....so....

 

(-4)^2 - 4(3)(k) < 0

16 - 12k < 0

16 < 12k

4/3 < k

k > 4/3

 

 

One real root if the disriminant = 0

(-4)^2 - 4(3)k = 0

16 - 12k = 0

16 = 12k

4/3 =  k 

 

It's obvious that we must have two real roots if  k < 4/3

 

 

 

cool cool cool

 Jun 9, 2019

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