Question

If a and b are the roots of the equation x2 + ax -b = 0, then value of a and b is​

Answer 1

Step-by-step explanation:

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Answer 2

Answer:

a = -1

b = 2

Step-by-step explanation:

Let the roots be $\alpha$ & $\beta$ respectively

where

$\alpha$ = a

$\beta$ = b               (given in the question that they are the roots of the equation)

p(x)= $x^{2} + ax - b$

a' = 1

b' = a

c' = -b

$\alpha + \beta$ = coefficient of b' / coefficient of a'

a + b  = $\frac{a}{1}$

a + b = a

b = -2a

$a = \frac{-b}{2}$                              (equation 1)

$\alpha \beta$ = coefficient of c' / coefficient of a'

ab = $\frac{-b}{1}$

$( \frac{-b}{2} )$b = -b                           (from equation 1)

$\frac{-b^{2} }{2}$ = -b

$\frac{-b^{2} }{-b}$ = 2

b = 2

putting the value of b in equation 1

a = $\frac{-b}{2}$

a = $\frac{-2}{2}$

a = -1

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