Question

Find the zero of a quadratic polynomial by activity

Answer 1

Activity

To find zeroes of a quadratic polynomials graphically.

Aim

To draw the graph of the quadratic polynomial and observe.

i) Shape of the curve when coefficient of x2 is positive.

ii) Shape of the curve when coefficient of x2 is negative.

iii) Its number of zeroes.

Materials Required

Graph sheets and maths kit.

Procedure

1. Consider the following quadratic polynomial p(x) of the form,

$a {x}^{2} + b {y}^{2} + c$

(see the attachments)

conclusion

1. The shape of the curve obtained by drawing the graph of a quadratic polynomial is a parabola.

2. When coefficient of x2 is positive (a>0). The parabola open upwards.

3. When coefficient of x2 is negative (a<0). The parabola opens downwards.

4. A polynomial of degree 2 is a quadratic polynomial has at most 2 zeroes.

Answer 2

The graph of p(x) is given below.

Clearly, from the graph x=−4,1 are zeros of p(x).

Verification:-

p(−4)=(−4)^2 +3 *−4−4=16−12−4=0

p(1)=(1)^2 +3*1−4=1+3−4=0