quadratic equation

38.
Let a, b be roots of quadratic equation 4x^2 - 8x + 3 = 0
a+b = -(-8)/4 = 2;
ab = 3/4
Then
1/a + 1/b = (a+b)/(ab) = 2/(3/4) = 8/3
(1/a)(1/b) = 1/(ab) = 1/(3/4) = 4/3
Therefore required equation is
3x^2 - 8x + 4 = 0

39.
Let a, b be roots of quadratic equation 2x^2 - 9x - 5 = 0
a+b = -(-9)/2 = 9/2;
ab = -5/2
Then
1/a + 1/b = (a+b)/(ab) = (4/2)/(-5/2) = -4/5
(1/a)(1/b) = 1/(ab) = 1/(-5/2) = -2/5
Therefore required equation is
5x^2 + 4x - 2 = 0

38.
Let the 2 roots be m and n, so
m + n = 2..........(1)
mn = 3/4...........(2)
1/m + 1/n = (m +n)/mn = 2/(3/4) = 8/3.
(1/m)(1/n) = 1/mn = 4/3.
So the equation is
x^2 - (8/3) x + 4/3 = 0
3x^2 - 8x + 4 = 0.
39.
Similarly, m + n = 9/2..........(1)
and mn = -5/2...............(2)
So (m +n )/mn = (9/2)/(-5/2) = -9/5.
1/mn = -2/5.
So the equation is
x^2 + 9x/5 - 2/5 = 0
5x^2 + 9x - 2 = 0.