The quadratic equation 2x2−3x−1=0 whose roots are increased by 2 is

A
$2 x^{2} - 11 x + 13 = 0$
B
$2 x^{2} - 5 x - 3 = 0$
C
$x^{2} - 5 x + 4 = 0$
D
$3 x^{2} + 5 x - 2 = 0$

Solution:

$R o o t s a r e i n c r e a s e d b y 2 i s f (x - 2) = 0 \Rightarrow 2 {(x - 2)}^{2} - 3 (x - 2) - 1 = 0 \Rightarrow 2 (x^{2} - 4 x + 4) - 3 x + 6 - 1 = 0 \Rightarrow 2 x^{2} - 8 x + 8 - 3 x + 5 = 0 \Rightarrow 2 x^{2} - 11 x + 13 = 0$

The quadratic equation $2 x^{2} - 3 x - 1 = 0$ whose roots are increased by 2 is

Solution:

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