The quarratic polynomial p(x) =ax2+bx+c has two diffrent roots including -2 The quadratic polynomial q(x)=ax2 +cx+b has two diffrent roots - Maths - Complex Numbers and Quadratic Equations

Question

The quarratic polynomial p(x) =ax2+bx+c has two
diffrent roots including -2 The quadratic polynomial
q(x)=ax2 +cx+b has two diffrent roots including 3 if
f&g r d other roots of p(x) and q(x) resp then find the value
of f/g

Ankush Jain · Accepted Answer

Given, quadratic polynomial are p(x) = ax2 + bx + c and q(x) = ax2 + cx + b The roots of p(x) are -2 and f whereas the roots of q(x) are 3 and g Taking p(x) = ax2 + bx + c, we get Product of roots = -2 Ã— f = $\frac{c}{a}$ â‡’ f = $\frac{- c}{2 a}$ (1) Similarly, on taking q(x) = ax2 + cx + b, we get â‡’ Product of roots = 3 Ã— g = $\frac{b}{a}$ â‡’ g = $\frac{b}{3 a}$ (2) On dividing (1) by (2), we get $\frac{f}{g} = \frac{\frac{- c}{2 a}}{\frac{b}{3 a}} = \frac{- 3 c}{2 b}$

The quarratic polynomial p(x) =ax2+bx+c has two diffrent roots including -2.The quadratic polynomial q(x)=ax2 +cx+b has two diffrent roots including 3.if f&g r d other roots of p(x) and q(x) resp. then find the value of f/g

The quarratic polynomial p(x) =ax²+bx+c has two diffrent roots including -2.The quadratic polynomial q(x)=ax² +cx+b has two diffrent roots including 3.if f&g r d other roots of p(x) and q(x) resp. then find the value of f/g