Consider a quadratic polynomial whose roots are and .

MATHEMATICS · Multi-part · CBSE · Mathematics · Polynomials · Polynomials

Problem

Consider a quadratic polynomial

ax^{2}+bx+c

(a\neq0)

whose roots are

\alpha

and

\beta

. (i) Express

b

and

c

in terms of

a

\alpha+\beta

and

\alpha\beta

. Give your answer in the simplest form. (ii) Explain how changing the value of the leading coefficient

a

while keeping

\alpha

and

\beta

unchanged affects the coefficients

b

and

c

. (iii) Let

\alpha+\beta=4

and

\alpha\beta=3

. Write the quadratic for

a=1

and for

a=5

, and comment on the difference between the two polynomials.