The value of b for which the sum of the squares of the roots of the equation x^{2}-(b-2)x-b-1=0 assumes the least value is

  • Option 1)

    0

  • Option 2)

    1

  • Option 3)

    2

  • Option 4)

    3

 

Answers (1)
P Prateek Shrivastava

As learnt in concept

Roots of Quadratic Equation with real Coefficients -

\alpha ,\beta are roots if

ax^{2}+bx+c= 0

is satisfied by x= \alpha ,\beta

 

- wherein

\alpha ,\beta\in C

a,b,c\in R

 

 

 And,

 

Sum of Roots in Quadratic Equation -

\alpha +\beta = \frac{-b}{a}

- wherein

\alpha \: and\beta are root of quadratic equation

ax^{2}+bx+c=0

a,b,c\in C

 

 And,

 

Product of Roots in Quadratic Equation -

\alpha \beta = \frac{c}{a}

- wherein

\alpha \: and\ \beta are roots of quadratic equation:

ax^{2}+bx+c=0

a,b,c\in C

 

 

\alpha ^{2}+ \beta ^{2}=(\alpha + \beta)^{2}-2 \alpha \beta

=(b-2)^{2}-2(-1)(b+1)

=b^2+4-4b+2b+2

=b^{2}-2b+6

=b^{2}-2b+1+5

=(b-1)^{2}+5

Minimum value at b=1


Option 1)

0

This option is incorrect.

Option 2)

1

This option is correct.

Option 3)

2

This option is incorrect.

Option 4)

3

This option is incorrect.

Exams
Articles
Questions