Question

Find the valus of a and b if the sum and the product of the roots of the equation 4ax2+4bx+3=0 are 1/2 and 3/16

Answer 1

Quadratic Equation = 4ax² + 4bx + 3 = 0 

Sum of zeros = 1/2 

Product of zeros = 3/16 

-b/a = sum of zeros 

-4b/4a = 1/2 
-84b    = 4a 
-21b    = a ----(1)

Product of zeros = c/a 

3/16 = 3/4a

1/16 = 1/4a 

4a = 16 

a = 4 


b = -2

Answer 2

Given 4ax²+4bx+3=0

a = 4 a

b = 4 b

c = 3


product of roots = 3/16

sum of roots = 1/2

Actually Product of roots = c/ a = 3/4a

Sum of roots = - b/ a = -4b / 4 a = - b / a

According to the problem,

=> 3/ 4 a = 3/16

=>4 a = 16

=> a = 4

And,


- b / a = 1/2

- b / 4 = 1/2

- b = 4/2

b = -2.


( a,b) = ( 4, -2)

hope helped!