A quadratic polynomial is given by

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

Problem

P(x)=ax^{2}+bx+9

. Its graph touches the

x

-axis at

x=3

. (i) Write the algebraic condition satisfied by the roots of a quadratic polynomial whose graph touches the

x

-axis at a single point. (ii) Using the condition from part (i) together with the information that

x=3

is the point of tangency, form the equations involving

a

and

b

. (iii) Solve the equations obtained in part (ii) to find the values of

a

and

b

, and hence write the complete expression for

P(x)