Asked by Helena
Given that the quadratic equation x^2-2x-m+1=0 has 2 positive real number roots, a and b, determine the range of the values of m.
Answers
Answered by
Damon
b^2-4ac is positive for real roots
4 - 4(1)(1-m) is positive
4 - 4 + 4 m is positive
or 4 m is positive
so m is positive
m>0 for sure
now
2 +/- sqrt (b^2-4ac) is positive for positive root
2 +/- sqrt(4-4(1-m) ) is positive
2 +/- sqrt(m) is positive
m < 4
so
0 <m< 4
4 - 4(1)(1-m) is positive
4 - 4 + 4 m is positive
or 4 m is positive
so m is positive
m>0 for sure
now
2 +/- sqrt (b^2-4ac) is positive for positive root
2 +/- sqrt(4-4(1-m) ) is positive
2 +/- sqrt(m) is positive
m < 4
so
0 <m< 4