Let be a quadratic polynomial whose zeros are and

MATHEMATICS · Subjective · CBSE · Mathematics · Polynomials · Polynomials

Problem

Let

p(x)

be a quadratic polynomial whose zeros are

\sqrt{5}

and

-\sqrt{5}

. Further, it is known that

p(1)=6

. (i) Determine the explicit expression for

p(x)

. (ii) Using the polynomial found in part (i), find the value of

p(2)

. (iii) Show that the coefficient of

x

in your polynomial is zero and give a reason based on the nature of the zeros.