Question

Let a, b, c, d be distinct real numbers such that a, b are roots of x² - 5cx - 6d = 0, and c, d are roots of x² − 5ax - 6b = 0. Then b + d is

(a) 180

(b) 162

(c) 144

(d) 126

Answer 1

Answer is : (c) 144

It is given that the quadratic equation

x² - 5cx - 6d = 0 has roots a and b, then

a + b = 5c …(i)

and ab = − 6d …(ii)

and, the quadratic equation

x² - 5ax − 6b = 0 has roots c and d, then

c + d = 5a …(iii)

and cd = − 6b …(iv)

Now, from Eqs. (i) and (iii), we have

∴ a and c are the roots of equations.

x² - 5cx - 6d = 0 and x²- 5ax - 6b = 0, respectively.

From Eqs. (i) and (iii), we have