. 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
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
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.
Similar questions