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x ^ 2 - ( k ) /(2) x = 2p In ...

` x ^ 2 - ( k ) /(2) x = 2p `
In the quadratic equation above, ` k and p ` are constants. What are the solutions for ` x ` ?

A

` x = (k ) /(4) pm (sqrt ( k^ 2 + 2 p )) /(4) `

B

` x = ( k ) /(4) pm (sqrt( k ^ 2 + 32 p ))/(4) `

C

` x = ( k ) /(2) pm ( sqrt ( k^ 2 + 2p )) /(2) `

D

` x = ( k ) /(2) pm (sqrt ( k ^ 2 + 32 p ) ) /(4 ) `

Text Solution

Verified by Experts

The correct Answer is:
B
The given quadratic equation can be rewritten as` 2x ^2 − kx − 4p = 0`. Applying the quadratic formula, ` ( -b pm sqrt ( b ^ 2 - 4ac )) /(2a ) `, to this equation with ` a = 2, b = -k and c = - 4p ` gives the solutions ` ( k)/(4 ) pm (sqrt (k^ 2 + 32p ))/( 4 ) `.
Choices A, C, and D are incorrect and may be the result of errors in applying the quadratic formula.
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