Question

Ifa, B are the zeros of the polynomials
p(x)=4x²+3x+7 then 1/a +1/b​

Answer 1

Answer:

1/a + 1/b = -3/7

Step-by-step explanation:

Given,

a and b are the zeroes of the polynomial .

Then, a = alpha, b = beta

p(x) = 4x^2 + 3x + 7

Here, a = 4, b = 3 , c = 7

We know that,

CASEI I -

(alpha) + (beta) = -b/a

=> a + b = -b/a

=> a + b = -3/4 ...(1)

CASE II -

(alpha)•(beta) = c/a

=> a•b = c/a

=> a•b = 7/4 ...(2)

Now according to the question,

1/a + 1/b = (a + b)/a•b ....(3)

Now from eq.(1) , eq.(2) and eq.(3) , we get

(a+b)/a•b = {(-3)/4} / {7/4} = -3/7

Hence,

1/a + 1/b = -3/7