Consider the quadratic polynomial

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

Problem

p(x)=x^{2}+4x+5

. Answer the following: (i) Write the expression for the discriminant

\Delta

of a general quadratic

ax^{2}+bx+c

. State the condition on

\Delta

for (a) two distinct real zeros, (b) exactly one real zero, and (c) no real zeros. (ii) Calculate the value of the discriminant for

p(x)

. Hence determine the nature and number of its zeros. (iii) Based on your answer to (ii), explain with reasoning whether the graph of

y=p(x)

intersects, touches, or stays completely above/below the

x

–axis.