1.

The positive value of `k`for which the equation `x^2+k x+64=0`and `x^2-8x+k=0`will both have real roots, is4 (b) 8(c) 12 (d) 16

Answer» Let `D_(1)" and "D_(2)` be the discriminants of the first and second given equations respectively.
For real roots, we must have `D_(1)ge0" and "D_(2)ge0.`
Now, `D_(1)ge0" and "D_(2)ge0`
`implies" "(4p^(2)-4xx64)ge0" and "(64-8p)ge0`
`implies" "p^(2)-64ge0" and "64-8pge0`
`implies" "p^(2)ge64" and "8pge64`
`implies" "pge8" and "ple8" "[because" p is positive"]`
`implies" "p=8.`
Hence, p=8.


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