Question

if alpha and beta are the roots of x^2-3 then alpha+beta and alpha -beta respectively are??​

Answer 1

Question :-

If α and β are the roots of x² - 3 , then α + β and αβ respectively are -

Concept :-

If a is the coefficient of x² , b is coefficient of x & c is constant and α and β are roots of the equation -

$\rm\purple{ \alpha + \beta = \frac{-b}{a}}$

$\rm\purple{ \alpha \beta = \frac{c}{a}}$

Solution :-

According to the question :-

• $\rm a = 1$
• $\rm b = 0$
• $\rm c = -3$

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

$\rm = \frac{0}{1}$

$\rm = 0$

• $\boxed{\rm \alpha + \beta = 0}$

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

$\rm = \frac{-3}{1}$

$\rm = -3$

• $\boxed{\rm \alpha \beta = -3}$

Hence the option (c) is correct