A quadratic polynomial ( ) is represented graphically by a parabola in the –plane.

MATHEMATICS · Multi-part · CBSE · Mathematics · Quadratic Equations · Quadratic Equations

Problem

A quadratic polynomial

p(x)=ax^{2}+bx+c

(

a\neq 0

) is represented graphically by a parabola in the

xy

–plane. (i) State the algebraic expression called the discriminant of

p(x)

in terms of

a,\,b

and

c

. (ii) Explain, without performing any numerical calculation, how the sign of the discriminant determines the number of real zeros of

p(x)

and the manner in which its graph meets the

x

–axis. (iii) The graph of a certain quadratic polynomial touches the

x

–axis at the point

(-4,0)

and opens upward. Using only the information given, predict the value (positive, zero or negative) of its discriminant and justify your answer.