Question 22
If $$f(x + 1) = x^2 - 3x + 2$$ and if the roots of the equation $$f(x) = 0$$ are $$\alpha$$ and $$\beta$$, then the value of $$\alpha^2 + \beta^2$$ is
Correct Answer: 13
Solution
Putting $$y = x + 1$$, so that $$x = y - 1$$, gives $$f(y) = (y-1)^2 - 3(y-1) + 2 = y^2 - 5y + 6$$. The roots of $$y^2 - 5y + 6 = 0$$ are 2 and 3, so $$\alpha^2 + \beta^2 = 4 + 9 = 13$$.
Get AI Help
Book Free CAT Mentorship
Get personalized CAT strategy from a 99%iler
500+ students mentored
OTP Verification
Enter the 6-digit code sent to your phone
Booking Summary
Session:Free CAT Mentorship
Phone:
Date:
Time:
Enter OTP
Didn't receive the OTP?
