Question

if alpha and beta are the zeroes of x2+7x+12 then find the value of 1/alpha+1/beta-2alpha beta

Answer 1

Answer:

step by step explanation

Answer 2

Answer:

The correct answer is $\frac{-295}{12}$.

Step-by-step explanation:

The given polynomial is $\left.x^{2}+7 x+12$

To find the value of  $&\frac{1}{\alpha}+\frac{1}{\beta}-2 \alpha \beta$.

Step 1

$\mathrm{Follow\:the\:PEMDAS\:order\:of\:operations}$

PEMDAS: Parentheses, Exponents, Multiplication, and Division (from left to right), Addition and Subtraction (from left to right).

Let $\alpha, \beta$ are zeros of a given polynomial

therefore,

Sum of zeros, $\alpha+\beta$ $=\frac{-7}{1}$$=-7$

and product of zeros, $\alpha \beta$ $=\frac{12}{1}$$=12$

Step 2

Now,

$&\frac{1}{\alpha}+\frac{1}{\beta}-2 \alpha \beta$

$&=\frac{\alpha+\beta}{\alpha \beta}-2 \alpha \beta$

Multiply and divide (left to right)

$&=\frac{-7}{12}-2(12)$

$&=\frac{-7}{12}-24$

Add and subtract (left to right)

$=\frac{-295}{12}$

Therefore, the correct answer is $\frac{-295}{12}$.

#SPJ2