Question

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if alpha and beta are the zeroes of the polynomial x²-8x+15 ,find the value of 1/alpha +1/beta without finding the zeroes.

Class10 (polynomials).​

Answer 1

Answer:

8/15

Step-by-step explanation:

Pol. written in form of x^2 - Sx + P represent the sum and product of roots as S and P respectively. So if α and β are roots :

  α + β = 8     &   αβ 15

In question :

⇒ 1/α + 1/β

⇒ ( β + α ) / αβ

⇒ ( sum of roots ) / product of roots

⇒ 8 / 15       { from above }

 hence the required value is 8/15

Answer 2

$\huge\underline\mathtt\red{Solution}$

$\underline\mathtt\blue{Given:}$

If $\alpha \: and \: \beta$ are zeros of the polynomial x² - 8x + 15, find the value of $\frac{1}{ \alpha } + \frac{1}{ \beta }$ without finding the zeros.

$\underline\mathtt\blue{To ~Find:}$

$\frac{1}{ \alpha } + \frac{1}{ \beta } =?$

$\rule {300}{2}$

We know ,

Sum of the roots

$\implies \alpha + \beta = 8$

Product of the roots

$\implies \alpha \beta = 15$

Now,

$\sf{= \frac{1}{ \alpha } + \frac{1}{ \beta }}$

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

$\sf{= \frac{8}{15}}$

Since,the required value is $\sf{= \frac{8}{15}}$

$\rule {300}{2}$

$\huge\underline\mathtt\pink{ThankYou}$