### Han Muyuan Alex's answer to Ang Tiong Boon'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:
2 months ago