WMA11 January 2020

5. WMA11/01 Edexcel IAL P1​​ January​​ 2020, Q5 (Algebraic Expressions)

(a) Find, using algebra, all solutions of​​ 

20x3 – 50x2  - 30x = 0 

(3)

(b) Hence find all real solutions of​​ 

20 y + 332  – 50( y + 3) - 30 y + 312 = 0 

(4)

SOLUTION

a-

2x3-5x2-3x=0

x2x2-5x-3=0

So, one of the​​ solution is x=0.​​ 

2x2-5x-3=0

2x+1x-3=0

2x+1=0      x-3=0

x= -12         x=3

Hence, the values of x are​​ 

x=-12,0,&3

b-

Always remember, when the word ‘hence’ is used in the question, it means we have to use the answer of prevous part and carry the calculations out for the next part of it. So,​​ from the above solution of​​ equation, we get x as ​​ -1/2, 0, & 3. Now, for the given expression, the solution of y+3 is equal to the above solutions, because this time in place of x, (y+3) has been substituted. ​​ 

When x= -1/2,​​ 

y+312 = -12 (Rejected)​​ 

This means square root of y+3 is equals to -1/2, which​​ is not possible. If you take a positive square root a number, it is always a positive number as an answer. Say, you take a positive square root of 4; the answer is +2, not -2. Therefore, there is no solution to it.​​ 

When x= 3,

y+312=3

y+3=9

y=6 

When x=0

y+312=0

y+3=0

y=-3

So, the real​​ solutions of the equations are​​ 

y=-3&6