Consider the quadratic polynomial (y=(k-2)x^ 2 +4x+k )

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

Problem

Consider the quadratic polynomial

y=(k-2)x^{2}+4x+k

, where

k

is a real parameter. (a) Find the condition on

k

for which the graph of the polynomial has exactly one

x

-intercept. (b) Find the condition on

k

for which the graph has no

x

-intercepts. (c) For a value of

k

that satisfies the condition in part (i), determine the

x

-coordinate of the single

x

-intercept.