hs's answer to Rosie's Secondary 3 A Maths Singapore question.
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x²+(1-p)x-p
b²-4ac >= 0 for real roots (if question didnt specify whether equal or distinct)
(1-p)²-4(1)(-p) >=0
1-2p+p² +4p >=0
p²+2p+1 >=0
complete the square from here
(p+2/2)²-(2/2)²+1 >=0
(p+1)² >=0
Since (p+1)² >= 0, the equation has real roots for all values of p.
b²-4ac >= 0 for real roots (if question didnt specify whether equal or distinct)
(1-p)²-4(1)(-p) >=0
1-2p+p² +4p >=0
p²+2p+1 >=0
complete the square from here
(p+2/2)²-(2/2)²+1 >=0
(p+1)² >=0
Since (p+1)² >= 0, the equation has real roots for all values of p.
Date Posted:
1 year ago
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