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The positive value of k for which x2 +Kx +64 = 0 & x2 - 8x + k = 0 will have real roots .
Ans: x2 + Kx + 64 = 0
⇒ b2 -4ac > 0
K2 - 256 > 0
K > 16 or K < - 16 ...............(1)
x2 - 8x + K = 0
64 - 4K > 0
⇒ 4K < 64
K < 16 ...............(2) From (1) & (2) K = 16
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Perform the denoted operation for each of the following. (a) Add 6x 5 -10x 2 + x - 45 to 13x 2 - 9 x + 4 . (b) Subtract 5x 3 - 9 x 2 + x - 3 from x 2+ x +1.
q5
4.2^2x+1 - 9.2^x + 1=0
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