Question

For what values of k, the equation 9x2+6kx+4=0 has equal roots?


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Answer 1

Answer:

Step-by-step explanation:

9x  

2

+6kx+4=0

equal roots so

b  

2

−4ac⩾0

(6k)  

2

−4(9)(4)⩾0

36k  

2

−36(4)⩾0

36(k  

2

−4)=0

k  

2

−4=0

k  

2

=2  

2

 

k=±2

Let us check

9x  

2

+6(2)x+4=0

9x  

2

+12x+4=0

9x  

2

+6x+6x+4=0

3x(3x+2)+2(3x+2)=0

(3x+2)(3x+2)=0

∴x=  

3

−2

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,  

3

−2

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