Let be a quadratic polynomial whose zeros are and

MATHEMATICS · Subjective · CBSE · Mathematics · Polynomials · Polynomials

Problem

Let

f(x)=2x^{2}+bx+c

be a quadratic polynomial whose zeros are

\alpha

and

\beta

. Given that

\alpha+\beta=5

and

\alpha\beta=4

, answer the following: (i) Find the values of

b

and

c

. (ii) Form the quadratic equation whose roots are

\dfrac1\alpha

and

\dfrac1\beta

and write it in the standard form

Ax^{2}+Bx+C=0

. (iii) Calculate the value of

\dfrac{1}{\alpha}+\dfrac{1}{\beta}

and verify that it equals

-\dfrac{B}{A}

for the equation obtained in part (ii).