Question

if alpha and beta are the zeros of the polynomial P of x is equal to X square + 12 x + 35 and find the value of one by Alpha Plus One by beta​

Answer 1

alpha+beta=-b/a

alpha+beta=-12

alpha*beta=c/a

alpha*beta=35

now,

1/alpha +1/beta

taking lcm

we get,

beta+alpha/alpha*beta

now put up the value

-12/35 is the answer

Answer 2

The value of $\dfrac{1}{\alpha}+\dfrac{1}{\beta}$ is $-\dfrac{12}{35}$.

Step-by-step explanation:

The given polynomial is

$P(x)=x^2+12x+35$

If a polynomial is defined as $P(x)=ax^2+bx+c$, then

Sum of zeroes = -b/a

Product of zeroes = c/a

In the given polynomial a=1,b=12 and c=35.

It is given that α and β are the zeros of the polynomial P(x).

$\alpha+\beta=-\dfrac{12}{1}$

$\alpha+\beta=-12$                .... (1)

$\alpha\beta=\dfrac{35}{1}$

$\alpha\beta=35$              .... (2)

We need to find the value of $\dfrac{1}{\alpha}+\dfrac{1}{\beta}$.

$\dfrac{1}{\alpha}+\dfrac{1}{\beta}=\dfrac{\beta+\alpha}{\alpha\beta}$

Substitute the values form equation (1) and (2).

$\dfrac{1}{\alpha}+\dfrac{1}{\beta}=\dfrac{-12}{35}$

Therefore, the value of $\dfrac{1}{\alpha}+\dfrac{1}{\beta}$ is $-\dfrac{12}{35}$.

#Learn more

If the sum of zeroes of polynomial p(x)=2x^2-kx+4is the same as the product of zeroes find the value of k.

https://brainly.in/question/4359355