Question

if alpha and beta are the zeros of the polynomial ax2+bx+c then find
1) alpha/beta+beta/alpha
2) alpha^2 + beta^2

Answer 1

ax²+bx+c
2)α²+β²
⇒we know that ,
⇒α+β= -b÷a
⇒squaring on both sides
⇒α²+β²+2αβ=b²÷a²
⇒α²+β²=b²÷a²-2αβ---------------------------eq 1

1)α÷β+β÷α
=α²+β²÷αβ
w.k.t,αβ=c÷a and substitute eq--1
=(b²÷a²-2αβ)÷(c÷a)
=(b²-2αβa²÷a²)÷(c÷a)
=b²-2αβa²÷a²×a÷c
=b²-2αβa²÷ac

Answer 2

Answer:

the fact or phenomenon of light, radio waves, etc. being deflected in passing obliquely through the interface between one medium and another or through a medium of varying density.

change in direction of propagation of any wave as a result of its travelling at different speeds at different points along the wave front.

measurement of the focusing characteristics of an eye or eyes.