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The value of \lambda such that sum of the squares of the roots of the quadratic eqaution, x^2 + (3-\lambda)x + 2 = \lambda has the least value is:

  • Option 1)

    \frac{15}{8}

  • Option 2)

    1

  • Option 3)

    2

  • Option 4)

    \frac{4}{9}

Answers (1)

best_answer

 

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

 

 

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

 

 

Quadratic Expression Graph when a > 0 & D < 0 -

No Real and Equal root of

f\left ( x \right )= ax^{2}+bx+c

& D= b^{2}-4ac

- wherein

Given quadratic equation 

x^{2}+(3-\lambda )x+2=\lambda

roots are \alpha  and  \beta

from the concept 

\alpha +\beta =\lambda -3    and   \alpha \beta =2-\lambda

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

                 =\lambda ^{2}+9-6\lambda -4+2\lambda

                =\lambda ^{2}-4\lambda +5

               =(\lambda-2) ^{2}+1

least value when \lambda=2

 

  

 


Option 1)

\frac{15}{8}

Option 2)

1

Option 3)

2

Option 4)

\frac{4}{9}

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