Question
Find the value of a such that the sum of the squares of the roots of the equation x^ 2 -(a-2) x-(a+1)=0 is least.
BITSAT
Mathematics
Quadratic Equation
2021
BITSAT 2021
BITSAT Mathematics Question (2021) — Solution
Options
- A. 4
- B. 2
- C. 1
- D. 3
Answer
C. 1
Step-by-step solution
Let , be the roots of the equation. + =a-2 and =-(a+1) Now, ^ 2 + ^ 2 =( + )^ 2 -2 =(a-2)^ 2 +2(a+1)=(a-1)^ 2 +5 ^ 2 + ^ 2 will be minimum if (a-1)^ 2 =0, i.e. a=1.
Related: Mathematics — Quadratic Equation · All PYQ Banks