Question

If alpha and beta are the zeroes of polynomial x^2+7x+12,then find the value of 1/alph+1/beta -2alphabeta. PLSSS ANSWER FAST. (Ans:alpha= -4,beta=-3,-295/12)

Answer 1

$p {x} \: = {x}^{2} + 7x + 12$
$\alpha + \beta = - b \: /\: a \\ \alpha \beta = c \: / \: a$
$1 \: / \: \alpha + 1/ \: \beta - 2 \alpha \beta = \alpha + \beta \: / \: \alpha \beta - 2 \alpha \beta$
$put \: these \: values\alpha + \beta = -7 \alpha \beta = 12$
=-7 /12 - 2×12
=-7-288/12
= 295/12
= 24.58
Alpha + beta = - 7.... 1
Alpha beta = 12
=>alpha = 12 / beta..... put in 1
12/beta + beta = - 7
12 + beta 2 = - 7beta
Beta2 + 7 beta +12 = 0
Beta = (-7 +1) /2 or (-7-1) /2
= - 4 or - 3
Put in
Alpha = - 4 or - 3
Hope it helps

Answer 2

Solution :

If α and β are the zeroes of the quadratic polynomial x² + 7x + 3

The value of (α - β)²

As we know that polynomial are compared with ax² + bx + c

a = 1

b = 7

c = 3

We now that sum of the zeroes;

We know that production of the zeroes;

Now;

We know that formula of the (α - β)² :

Thus;

The value of (α - β)² = 37.