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Question
If the equation x2 − bx + 1 = 0 does not possess real roots, then
Options
−3 < b < 3
−2 < b < 2
b > 2
b < −2
Solution
The given quadric equation is `x^2 - bx + 1 = 0`, and does not have real roots.
Then find the value of b.
Here, a = 1, b = -b and ,c = 1
As we know that `D = b^2 - 4ac`
Putting the value of a = 1, b = -b and ,c = 1
`=(-b)^2 - 4 xx 1 xx 1`
`=b^2 - 4`
The given equation does not have real roots, if D < 0
`b^2 - 4 < 0`
`b^2 < 4`
`b< sqrt4`
`b< ±2`
Therefore, the value of -2 < b< 2 .
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