Question

Calculate delta of x^2 -(m-1)x +m+2=0 And find its sign according to the value of m Deduce the value of m so that thr equation admits 2 distinct root

Answer 1

The delta of a quadratic is its discriminant, which in this case is:

(m-1)²-4(m+2)=m²-2m+1-4m-8=m²-6m-7=(m-7)(m+1).

Delta<0 (negative) when -1<m<7 and delta≥0 (positive) when m≤-1 or m≥7.

When m=7 or -1, the quadratic has two distinct roots.

The roots of x²-6x+9=0=(x-3)² or x²+2x+1=0=(x+1)², making the roots x=3 or -1.

That is: x=(m-1)/2 because delta=0.