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If the equation `x^(2)+5kx+16=0` has no real roots then

Answer» The given equation is `x^(2)+5kx+16=0.`
This is of the form `ax^(2)+bx+c=0,` where a=1, b=5k and c=16.
`:." "D=(b^(2)-4ac)=(25k^(2)-4xx1xx16)=(25k^(2)-64).`
Since, the given equation has no real root, we have
`:." "D=(b^(2)-4ac)=(25k^(2)-4xx1xx16)=(25k^(2)-64).`
`implies" "k^(2)lt(64)/(25)impliesk^(2)lt((8)/(5))^(2)`
`implies" "(-8)/(5)ltklt(8)/(5).`
Hence, the required real values of k are such that `(-8)/(5)ltklt(8)/(5).`


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