Question

if a and b are zeroes of the polynomial p(x)=4x²+3x+7,then 1/a+1/b is equal to​

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Given,

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

a and b are the zeroes of the polynomial.

The coefficient of x^2 = 4

The coefficient of x = 3

and constant term = 7

We know that,

alpha + beta = -b/a = coefficient of x/coefficient of x^2

so, a + b = -3/4

and alpha × beta = c/a = constant term/coefficient of x^2

a×b = 7/4

By using the identity:

1/alpha+1/beta = alpha + beta/alpha×beta

so now, 1/a+1/b = a+b/ab

substitute the values of ab and a+b.

-3/4÷7/4

-3/4×4/7

-3/7

Therefore the value of 1/a+1/b = -3/7.