Question

find the values of a and b, if the sum and the product of the roots of the equation 4ax^2+4bx+3=0 are 1/2 and 3/16 respectively

Answer 1

The equation is 4ax²+4bx+3=0
Here, a=4a, b=4b, c=3
Let, @&ß be the roots of the equation.

asper given condition, @+ß = 1/2, @ß= 3/16

@+ß=-b/a
1/2 = -4b/4a
1/2 = -b/a
a = -2b (i)

@ß = c/a
3/16 = 3/4a
a = 4
SUBSTITUTING IN (i)

-2b = a
-2b = 4
-b = 2
b = -2

SO, a=4, b=-2

Answer 2

Step-by-step explanation:

given that alpha + beta = 1/2 and alpha × beta = 3/16

eq 4ax2 + 4bx + 3 = o

alpha + beta = -b / a

putting value of alpha and beta

1/2 = - b/ a

a = -2b

alpha × beta = c/ a

putting value of alpha and beta

3/16 =3/4 a

a = 4

b = -2