Question

If alpha and beta are the zeros of the polynomial 4x square-16x+15, form a polynomial whose zeros are alpha by beta,beta by alpha

Answer 1

Find the zeros of 5x square-4x-8x and verify the relationship between zeros and coefficient

Answer 2

roots of 4x^2-16x+15=0 are a and b, (for alpha and beta)

by the properties of roots of a quadratic
a+b = -(-16/4) = 4
ab = 15/4

new roots: a/b and b/a
sum of new roots = a/b + b/a
= (a^2 + b^2)/(ab)

now a^2 + b^2 = (a+b)^2 - 2ab
= 4^2 - 2(15/4) = 17/2

so sum of new roots
= (17/2)/(15/4) = 34/15
product of new roots
= (a/b)(b/a) = 1

new equation: x^2 - 34/15 x + 1 = 0
15x^2 - 34x + 15 = 0

2nd question:

5x^2 - 4x - 8x = 0
5x^2 - 12x = 0
x(5x - 12) = 0
x = 0 or x = 12/5

I suspect a typo