Quadratic Equations with Parameters

Submitted by ladislav.foltyn on Sat, 04/20/2019 - 13:43
Project ID: 
6000000056
Accepted: 
SubArea: 
Equations and inequalities with parameters
Type: 
Match
Layout: 
6x6
Question: 
The equations with variable x and parameter m are given. For every equation find such set of all possible values of m, that the given equation has exactly one solution.
Questions Title: 
Equations:
Answers Title: 
Sets of values of parameter m:
Question 1: 
x2+2mx+4=0
Answer 1: 

{−2;2}

Question 2: 
mx2−2x+m=0
Answer 2: 

{−1;0;1}

Question 3: 
4(x+m)2=x2+m
Answer 3: 

{0;−34}

Question 4: 
x2m+4=3(m+2)
Answer 4: 

{−23}

Question 5: 
2x2+3xm+2=0
Answer 5: 

{−43;43}

Question 6: 
x2−2mx+1=0
Answer 6: 

{−1;1}

Tex: 
%tiket 32823 \NastavOT{2} \NastavOD{3}