Question

If alpha and beta are the Zeroes of the polynomial p(x)=5x^2- 7x +1, then find the value of (alpha/beta +beta/alpha)​

Answer 1

Answer:

alpha+beta=-7/5

alpha*beta=-1/5

by the question

( alpha+beta)^2-2alpha.beta

/aplha. beta

=- 59/5

Answer 2

Given:

The zeroes of the polynomial P(x) = 5x² - 7x + 1 is α and β

To be found:

The value of $\frac{1}{\alpha}+\frac{1}{\beta}$

Now,

Simplifying,

$\boxed{\frac{1}{\alpha}+\frac{1}{\beta}}$

$\implies \frac{\beta+ \alpha}{\alpha \beta}$

So,

α + β = sum of zeroes

αβ = product of zeroes

• We know that,

Sum of zeroes = $\boxed{\frac{-b}{a}}$

And

Product of zeroes = $\boxed{\frac{c}{a}}$

So,

From the polynomial,

P(x) = 5x² - 7x + 1

We will get

a = 5 , b = (-7) , and c = 1

Now,

Sum of zeroes (α + β) = $\boxed{\frac{-b}{a}}$ = $\bf \frac{-(-7)}{5} = \frac{7}{5}$

And

Product of zeroes (αβ) = $\boxed{\frac{c}{a}}$ = $\bf \frac{1}{5}$

Therefore,

$\boxed{\frac{1}{\alpha}+\frac{1}{\beta}}$

$= \frac{\beta+ \alpha}{\alpha \beta}$

$\bf = \frac{\frac{7}{5}}{\frac{1}{5}} = \frac{7}{5} \div \frac{1}{5}$

$= \frac{7}{ \not{5}} \times \not{5}$

= 7

Hence,

$\boxed{\red{\frac{1}{\alpha}+\frac{1}{\beta} = 7}}$