The sum of the roots of the equation x2+px+q=0 is equal to the sum of their squares, then

The sum of the roots of the equation $x^{2} + p x + q = 0$ is equal to the sum of their squares, then

A
$p^{2} - q^{2} = 0$
B
$p^{2} + q^{2} = 2 q$
C
$p^{2} + p = 2 q$
D
$q^{2} + q = 2 p$

Solution:

$x^{2} + p x + q = 0$

as per sum

$α + β = α^{2} + β^{2}$

$α + β = {(α + β)}^{2} - 2 α β$

$\Rightarrow - p = {(- p)}^{2} - 2 q$

$\Rightarrow p^{2} + p = 2 q$

Related content

NCERT Books for Class 10- Download Free PDF (2023-2024)

NCERT Books for Class 11- Download Free PDF (2023-2024)

USA Full Form – United States of America

NRC Full Form – National Register of Citizens

Distance Speed Time Formula

Refractive Index Formula

Electric Current Formula

Ohm’s Law Formula

Wavelength Formula