Question

Find the values of k for which the roots are real and equal in each of the following equations:
(i) kx²+4x+1=0
(ii) kx²-25x+4=0
(iii) 3x²-5x+2k=0
(iv) 4x²+kx+9=0
(v) 2kx²-40x+25=0
(vi) 9x²-24x+k=0
(vii) 4x²-3kx+1=0
(viii) x²-2(5+2k)x+3(7+10k)=0
(ix) (3k+1)xV+2(k+1)x+k=0
(x) kx²+kx+1=-4x²-x
(xi) (k+1)x²+2(k+3)x+(k+8)=0
(xii) x2 – 2kx + 7x + 1/4 = 0
(xiii) (k+1)x²-2(3k+1)x+8k+1=0
(xiv) 5x²-4x+2+k(4x²-2x-1)=0
(xv) (4-k)x²+(2k+4)x+(8k+1)=0
(xvi) (2k+1)x²+2(k+1)x+(k+4)=0
(xvii) 4x²-2(k+1)x+(k+4)=0
(xviii) x²-2(k+1)x+k²=0
(xix) k²x²-2(k-1)x+4=0
(xx) (k+1)x²-2(k-1)x+1=0
(xxi) 2x²+kx+3=0
(xxii) kx(x-2)+6=0
(xxiii) x²-4kx+k=0
(xxiv) kx(x-2√5)+10=0
(xxv) px(x-3)+9=0
(xxvi)4x²+px+3=0

Answer 1

Answer:

given the hint.

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