Math, asked by kekekeerthi053, 7 months ago

. If alphaand beta are the zeroep of the quadratic polynomial p(x)=5x^2-7x+1
find the value of 1/alpha+ 1/beta​

Answers

Answered by abhi569
24

Answer:

7

Step-by-step explanation:

Polynomials in form of k(x^2 - Sx + P) represent S as sum of roots and P as product of roots.

Here, 5x^2 - 7x + 1   ⇒ 5[ x^2 - (7/5)x + (1/5) ]

So, if a and b are roots,

⇒ a + b = 7/5        ⇒ ab = 1/5

Hence,

⇒ (1/a) + (1/b)

⇒ (a + b)/ab

⇒ (7/5) / (1/5)

⇒ 7/1

⇒7

Answered by Anonymous
23

Step-by-step explanation:

Let's denote alpha by x and beta by y. And x and y are the zeros of the polynomial.

So, we have to find the value of 1/x + 1/y.

Given polynomial: 5x² - 7x + 1 where a is 5, b is -7 and c is 1.

Sum of zeros = -b/a

x + y = -(-7)/5

x + y = 7/5

Product of zeros = c/a

xy = 1/5

Now,

→ 1/x + 1/y = (x + y)/xy

Substitute the values,

→ (7/5)/(1/5)

→ 7

Hence, the value of 1/alpha + 1/beta is 7.

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