Question

If the equation $a{x}^2+bx+c=x$ has no real roots, then the equation $a(a{x}^2+bx+c{)}^2+b(a{x}^2+bx+c)+c=x$ will have

• A. four real roots
• B. no real roots
• C. at least two real roots
• D. none of these

Answer 1

Answer: (B)

no real roots

Given that, $a{x}^2+bx+c=x$ ...(1)
Now, $a(a{x}^2+bx+c{)}^2+b(a{x}^2+bx+c)+c=x$ ...(2)
From (1), we get $a{x}^2+bx+c=x$
Therefore, eq. (2) also have no roots.
Ans: B