Question

If alpha& beta are the zeroes of the polynomial 2x2-7x+3. Find the sum of the reciprocal of its zeroes

Answer 1

You are probably dealing with the properties of the sum and product of roots of quadratic equations.
I will use a and b instead of alpha and beta

for 2x^2 - 7x + 3 = 0
the sum of the roots
= a+b
= 7/2
product = ab
= 3/2

so the reciprocals of the roots are 1/a and 1/b
new sum = 1/a + 1/b = (a+b)/(ab)
= (7/2) / (3/2) = 7/3
new product = (1/a)(1/b) = 1/(ab)
= 2/3

new equation:
x^2 - 7/3x + 2/3 = 0
or
3x^2 - 7x + 2 = 0

looking back, looks like I could have stopped after finding the new sum

Answer 2

Ghanta

Answer 3

this answer is correct.