Question

if alpha and better are the roots of the equation x²minus2x minus3≈0, find the value of alpha plus better, alpha better and 1÷alpha, 1÷better

Answer 1

Step-by-step explanation:

x² - 2x - 3 = 0

alpha + beta = -(-2)/1 = 2/1 = 2

alpha*beta = -3/1 = -3

(alpha - beta)² = (alpha+beta)² - 4alpha*beta

= 4 - 4(-3)

= 4 + 12 = 16

alpha - beta = 4

alpha + beta = 2

2 alpha = 6

alpha = 3

beta = alpha - 4 = 3-4 = -1

1/alpha = 1/3

1/beta = 1/-1 = -1

Answer 2

${\bold{\underline{\underline{Answer:}}}}$

${\bold{\therefore \alpha+\beta=2}}$

${\bold{\therefore \alpha\beta=-3}}$

${\bold{\therefore \frac{1}{\alpha}=\frac{1}{3}}}$

${\bold{\therefore \frac{1}{\beta}=-1}}$

${\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\underline\bold{Given : } \\ \implies \alpha \: and \: \beta \in \:( {x}^{2} - 2x - 3 = 0) \\ \\ \underline\bold{To \: Find : } \\\implies \alpha + \beta = ? \\ \\ \implies \alpha \beta = ?\\ \\ \implies \frac{1}{ \alpha } = ? \\ \\ \implies \frac{1}{ \beta } = ?$

• According to given question :

$\bold{Using \: middle \: term \: splitting :} \\ \implies {x}^{2} - 2x - 3 = 0 \\ \\ \implies {x}^{2} - 3x + x - 3 = 0 \\ \\ \implies x(x - 3) + 1(x - 3) = 0 \\ \\ \implies (x + 1)(x - 3) = 0\\ \\ \implies \alpha = 3 \\ \\ \implies \beta = - 1 \\ \\ \bold{For \: finding \: values : } \\ \bold{\implies \alpha + \beta = 3 + ( - 1) = 3 - 1 = 2 }\\ \\ \bold{\implies \alpha \beta = 3 \times - 1 = - 3 }\\ \\ \bold{\implies \frac{1}{ \alpha } = \frac{1}{3}} \\ \\ \bold{\implies \frac{1}{ \beta } = \frac{1}{ - 1} = - 1}$