Question

for what values of a and b,x=3/4 and x=-2 are the solutions of the equation ax२+bx-6=0

Answer 1

Given Quadratic equation is ax^2 + bx - 6 = 0.

Given roots of the equation are x = -3/4 and x = -2.

(i) when x = -3/4 then the equation will be 

 a(3/4)^2 + b(3/4) - 6 = 0

9a/16 + 3b/4 - 6 = 0

9a + 12b - 96 = 0 

3a + 4b - 32  = 0

a = 32 - 4b/3----------- (1)


(ii) when x = -2 then the equation will be

a(-2)^2 + b(-2) - 6 = 0

4a - 2b - 6 = 0

2a - b - 3 = 0   

2a - b = 3 ---------- (2)

Substitute (1) in (2), we get

2(32 - 4b/3) - b = 3

2(32 - 4b) - 3b = 9

64 - 8b - 3b = 9

64 - 11b = 9

-11b = -55

b = 5  


Substitute b = 5 in (2), we get

2a - b = 3

2a - 5 = 3

2a = 8

a = 8/2

a = 4.

Therefore the value is a = 4.

                  the value of b = 5.


Hope this helps!