WMA11 Jan 2019

9. WMA11/01 Edexcel IAL P1 January 2019, Q9 (Equations and Inequalities: Quadratic Inequalities)

The equation​​ 

3x + 5 = -2x + c 

where c is a constant, has no real roots.

Find the range of possible​​ values of c.​​ 

(7)

SOLUTION

3x+5= -2x+c

3+5x=-2x2+cx

2x2+5x-cx+3=0

2x2+5-cx+3=0

Since the question says that the equation has no real solution, using the second point above in the flash card. ​​ 

Finding the discriminant, where a=2, b=(5-c), and c=3. ​​ 

b2-4ac<0

5-c2-423<0

25-10c+c2-24<0

c2-10c+1<0

Finding the critical values of the equation above.​​ 

c2-10c+1=0

c-52-25=-1

c-52=24

c-5= ±24

c=5±26

Since the sign of inequality was less than, therefore, we will choose those values that are below the x–axis.​​ 

Thus,​​ the range of possible values of c is​​ 

5-26<c<5+26