Question

Alpha and beta are the roots of ax square +bx+c=0 then find the value of
(1/a alpha+b + 1/a beta+b)

Answer 1

alpha and beta are the roots (zeros ) of
ax² + bx + c = 0
products of roots = c/a
alpha.beta = c/a

sum of roots = -b/a
alpha + beta = -b/a

a.alpha + a.beta = -b

a.alpha + b = - a.beta ----(1)
a.beta + b = - a.alpha -----(2)

put equations (1) and (2) in
1/(a.alpha + b) + 1/(a.beta + b)

= 1/-a.beta + 1/-a.alpha

= - 1/a{ alpha + beta }/alpha.beta

= -1/a( -b/a)/(c/a)

= b/ca

Answer 2

Hi friend,

alpha and beta are the roots of the polynomial, (roots = zeroes)

ax²+bx+c = 0

Relationship between the zeroes and coefficients:-

Product of zeroes = alpha×beta =c/a

Sum of zeroes = alpha+beta = -b/a

a(alpha+beta) = -b

a.alpha + a.beta = -b

a.alpha + b = -a.beta

a.beta + b = -a.alpha

Substitute these values in

→ {1/a.alpha+b + 1/a.beta+b}

→ (1/-a.beta + 1/-a.alpha)

→ -1/a(alpha+beta)/alpha.beta

→ -1/a(-b/a)/(c/a)

→ -1/a(-b/a)(a/c)

→ bc/a

Hope it helps