Question

If the sum of the roots of quadratic equation is 2 and the sum of their reciprocal is 18/5 find the equation

Answer 1

Answer:

9$x^{2}$ -18$x$+5 =0

Step-by-step explanation:

a$x^{2}$+b$x$+c = 0 -----(i)

lets say roots are x,y

sum of the roots = -b/a = 2 =x+y

sum of the reciprocals of the roots are 1/x + 1/y = 18/5

(x+y)/xy = 18/5

2/xy = 18/5

xy = 5/9 = c/a product of the roots

therefore a=9 and c=5

then -b/a =9*2/9 =18/9

-b = 18

b = -18

now substitute in (i)

9$x^{2}$ -18$x$+5 =0