Question

if alpha and beta are zeros of polynomial f(x)=5x2 -7x+1 find the value of 1/alpha +1/beta​

Answer 1

Answer:

(1/a +1/)

1/a +1/B= (a + B/ ab)

(a + B)=-b/a = 7/5

ab = c/a = 2/5

so, (a + B/ab (7/5) /(2/5)

7/2

So, 1/a +1/b = (a + B/ ab = 7/2

Hence, 1/a +1/b = 7/2

Answer 2

Answer:

The value of ${1}/{\alpha} +{1}/{\beta}=7$.

Step-by-step explanation:

Given the polynomial $f(x)=5x^2 -7x+1$

$\alpha$  and $\beta$ are the zeros of the polynomial.

Sum of the roots of a polynomial is given by,

$\alpha +\beta=\dfrac{-b}{a}$

Thus, the sum of the roots in the given polynomial is

$\alpha +\beta=\dfrac{-(-7)}{5}=\dfrac{7}{5}$                                                              ...(1)

Product of the roots of a polynomial is given by,

$\alpha \beta=\dfrac{c}{a}$

Thus, the product of the roots in the given polynomial is

$\alpha\beta=\dfrac{1}{5}$                                                                                 ...(2)

Product of the roots of a polynomial is given by,

Given to find the value of

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

Substituting the values from equation (1) and (2),

$\dfrac{\beta+\alpha}{\alpha\beta}=\dfrac{\dfrac{7}{5} }{\dfrac{1}{5} }$

$=\dfrac{7}{5} }\times {\dfrac{5}{1} }=7$

Therefore, the value of ${1}/{\alpha} +{1}/{\beta}=7$.