Verified answer

Réponse :

1) Let f(m) = -4m² + 8m + 12

=> f'(m) = -8m+8

At turning point, m=1

f(m) is increasing in the interval ]-∞, -1[ U ]3, ∞[

f(m) is decreasing in the interval ]-1, 3[

2) For P(x) to have double roots, ∆=b²-4ac=0

=> (2m+2)²-4(2)(m²-1)=0

=> 4m²+8m+4-8m²+8=0

=> -4m²+8m+12=0

=> m= -1 or m=3

For m= -1, => 2x² = 0

=> x = 0

For m= 3, => 2x²+8x+8 = 0

=> x = 2

3) For P(x) to have distinct roots, ∆=b²-4ac>0

=> 2m+2)²-4(2)(m²-1)>0

=> 4m²+8m+4-8m²+8>0

=> -4m²+8m+12>0

=> -1 < m < 3

the possible values of m are { 0, 1, 2}