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Find the values of \( k \) for which the roots are real and equal in each of the following equations:
(i) \( k x^{2}+4 x+1=0 \)
(ii) \( k x^{2}-2 \sqrt{5} x+4=0 \)
(iii) \( 3 x^{2}-5 x+2 k=0 \)
(iv) \( 4 x^{2}+k x+9=0 \)
(v) \( 2 k x^{2}-40 x+25=0 \)
(vi) \( 9 x^{2}-24 x+k=0 \)
(vii) \( 4 x^{2}-3 k x+1=0 \)
(viii) \( x^{2}-2(5+2 k) x+3(7+10 k)=0 \)
(ix) \( (3 k+1) x^{2}+2(k+1) x+k=0 \)
(x) \( k x^{2}+k x+1=-4 x^{2}-x \)
(xi) \( (k+1) x^{2}+2(k+3) x+(k+8)=0 \)
(xii) \( x^{2}-2 k x+7 k-12=0 \)
(xiii) \( (k+1) x^{2}-2(3 k+1) x+8 k+1=0 \)
(xiv) \( 5 x^{2}-4 x+2+k\left(4 x^{2}-2 x-1\right)=0 \)
(xv) \( (4-k) x^{2}+(2 k+4) x+(8 k+1)=0 \)
(xvi) \( (2 k+1) x^{2}+2(k+3) x+(k+5)=0 \)
(xvii) \( \quad 4 x^{2}-2(k+1) x+(k+4)=0 \)
(xviii) \( 4 x^{2}-2(k+1) x+(k+1)=0 \)
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