Han Muyuan Alex's answer to Ryan's Secondary 3 A Maths Singapore question.
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To find define the number of real roots, use the formula b²-4ac; where a, b and c are from ax²+bx+c; if:
i) b²-4ac<0 then the equation has no real roots
ii) b²-4ac=0 to then the equation has 1 repeating real root
iii) b²-4ac>0 then the equation 2 different, real roots
as such, for the equation, x²-10x+(4-m)>0
a=1; b= -10; c=4-m, hence for b²-4ac<0
(-10)²-4(1)(4-m)<0
100-4(4-m)<0
100-16+4m<0
84+4m<0
4m<-84
m<-21
i) b²-4ac<0 then the equation has no real roots
ii) b²-4ac=0 to then the equation has 1 repeating real root
iii) b²-4ac>0 then the equation 2 different, real roots
as such, for the equation, x²-10x+(4-m)>0
a=1; b= -10; c=4-m, hence for b²-4ac<0
(-10)²-4(1)(4-m)<0
100-4(4-m)<0
100-16+4m<0
84+4m<0
4m<-84
m<-21
Date Posted:
1 year ago
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