Question

If alpha and beta are the zeros of polynomial x^2+ 7 x + 12 then find the value of 1/alpha + 1/ beta- 2 ×alpha×beta

correct answer will be mark as brainliest ​

Answer 1

We have,

${x}^{2} + 7x + 12 = 0\\ = > {x}^{2} + 4x + 3x + 12 = 0\\ = > x(x + 4) + 3(x + 4) = 0\\ = > (x + 3)(x + 4) = 0$

From this, we get alpha = -3 and beta = -4

Hence,

$\frac{1}{ \alpha } + \frac{1}{ \beta } - 2 \alpha \beta \\ = - \frac{1}{3} - \frac{1}{4} - 24 \\ = \frac{ - 4 - 3 - 288}{12} \\ = \frac{ - 295}{12}$

HOPE THIS COULD HELP!!!

Answer 2

$\huge \bold \red{heya \: friend}$

In the given polynomial,

a=1, b=7 and c=12

First, we will calculate the 2 zeroes by factorisation,

x²+7x+12=0

x²+3x+4x+12=0

x(x+3)+4(x+3)=0

(x+3)(x+4)=0

Hence, the 2 zeroes are

-3 and -4.

Now, sum of the zeroes,

$\alpha + \beta =$

-b/a= -7/1= -7

Product of the zeroes,

$\alpha \beta =$

c/a=12/1=12

Now,we will calculate the value of 1/alpha+1/beta-2 alpha.beta

♦1/alpha+1/beta-2 alpha.beta

♦beta+alpha/alpha.beta-2alpha.beta

♦alpha+beta/alpha.beta-2alpha.beta

♦-7/12-2(12)

♦-7/12-24

Taking the LCM of 12 and 1,

♦-7-288/12

♦-295/12

Therefore,

Answer: -295/12