Skip to content
dronacharya.ai
← JEE Main 2022 · 26 Jul · Shift 2
MathematicsSingle correct+4 / -1Question 1 of 90

JEE Main 2022 · 26 Jul · Shift 2, Mathematics question 1

The minimum value of the sum of the squares of the roots of x2+(3−a)x+1=2ax^2+(3-a)x+1=2a is:

Choose one option
Answer and worked solution

Official answer: C

Vieta. Write it as x2+(3−a)x+(1−2a)=0x^2+(3-a)x+(1-2a)=0: sum a−3a-3, product 1−2a1-2a.

Sum of squares =(a−3)2−2(1−2a)=a2−2a+7=(a−1)2+6=(a-3)^2-2(1-2a)=a^2-2a+7=(a-1)^2+6, least value 6 at a=1a=1.

(C)

Topics:Roots and coefficientsQuadratic expressions
Next question →