Question

# For what values of ‘p’ would the equation x2+2(p−1)x+p+5=0 possess at least one positive root?[ , -5][1, ][;, -1][2, ]

Solution

## The correct option is A [ , -5]For an equation to have positive roots D must be greater than '0'. Now D from the equation =4(p−1)2−4(1)(p+5)=4p2−12p−16 =4(p2−3p−4)=4(p−4)(p+1) ∴4(p−4)(p+1)>0......(1) So, D is positive in the region (−∞,−1) and (4,∞). x=−b+√D2a≥0 ⟹D≥b2 b2=4(p−1)2 ∴p2−3p−4≥p2+1−2p ⟹p≤−5..........(2) Taking intersection of equation (1) and (2), we get - p lies from (−∞,−5].

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