Q41 / 90 · JEE Main 2019 (10 Jan Shift 2) · Mathematics

The value of $λ$ such that sum of the squares of the roots of the quadratic equation, $x^{2} + (3 - λ) x + 2 = λ$ has the least value is:

Correct answer
A
$2$
B
$\frac{4}{9}$
C
$\frac{15}{8}$
D
$1$

Solution

We have, $x^{2} + (3 - λ) x + 2 = λ, have roots α & β .$

Then, $f (λ) = α^{2} + β^{2}$

$= {(α + β)}^{2} - 2 α β = {(3 - λ)}^{2} - 2 (2 - λ) = λ^{2} - 6 λ + 9 - 4 + 2 λ = λ^{2} - 4 λ + 5$

$f^{'} (λ) = 2 λ - 4 = 0$ ${$ for the minimum value of $f (λ)}$

As $f^{''} (λ) = 2 > 0$

$\Rightarrow λ = 2$

Hence, the correct answer is option: 'A'.

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The value of λ such that sum of the squares of the roots of the quadratic equation, x2+3-λ x+2=λ has the least value is:

Solution

More Quadratic Equation Questions

The value of $λ$ such that sum of the squares of the roots of the quadratic equation, $x^{2} + (3 - λ) x + 2 = λ$ has the least value is: