Question

If not the roots of the equation x^2-(m+1)x+(m+4)=0 are negative ,then what is the interval for value of m?

Answer 1

x² - (m+1)x + m + 4 = 0

If the equation has ral roots, then the discriminant must be positive:

Let us verify:

d = b² - 4ac > 0

==> (m+1)² - 4*1* (m+4) > 0

==> m² + 2m + 1 - 4m - 16 > 0

==> m² -2m - 15  > 0

==> (m-5)(m+3) >0

==> m-5 > 0   and (m+3)>0   OR (m-5)< 0  and m+3 < 0

==> m > 5  and m > -3 OR m<5 and m<-3