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
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Answered by
36
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
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
Answered by
6
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
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