Question

The ratio of the roots of the
equation ax²+bx+c = 0 is
r:1. Prove that b²r= ac (r+1)²​

Answer 1

Answer:

Hence Proved

Step-by-step explanation:

i) Let the two roots of the given quadratic equation be α & β;

then as given  α/β = r; ==> α = β*r ---------- (1)

ii) By properties of roots of quadratic equation,

Sum of roots: α + β = -b/a;  

Substituting from (1), α = β*r,  β(1 + r) = -b/a;

Squaring,  β²(1 + r)² = b²/a² --------- (2)

and Product of roots, α*β = c/a

Again substituting from (1) for α = β*r, β²*r = c/a ----- (3)

iii) Dividing (2) by (3): (1 + r)²/r = b²/ac

Cross multiplying, {(1 + r)²}*(ac) = (b²)*(r)