Question

Some students were playing in the park by throwing paper balls in the sky. Graph of the path followed by paper ball thrown by Ankit is shown in the figure. Answer any four questions based on this graph p(x).​

Answer 1

Answer:

it is very difficult but i ought to try it but couldn't

Answer 2

Answer:

1. The vertex of the graph is Option B (-3,1)
2. The zeros of the graph are Option B (-2,-4)
3. Quadratic equation of polynomial is option D
4. The sum of $\alpha ^{2}+\beta ^{2}$ is option A (20)
5. The new polynomial formed, when roots are doubled is option A

Step-by-step explanation:

1. By using the coordinate geometry, The vertex of the graph is found to be at (-3,1)
2. In the graph, for y =0, the value of x is -2 nd -4. Thus,-2 and -4 are zeros of the Graph where the value of the y is zero.
3. The quadratic equation can be formed by the sum and product of roots.    The equation is given by

       $x^{2} -(Sum)x+Product=0$

• The sum of roots is $-2-4=-6$

• The product of roots is $(-2)*(-4)=8$

       $x^{2}+ 6x+8=0$

     4. The sum of  

        $=\alpha ^{2}+\beta ^{2} \\=(-4)^{2}+\(-2) ^{2}\\=20$

     5. If roots are doubled, the roots become -8,-4

• Sum of roots=-12

• Product=32

• The equation is given by

        $x^{2} -(Sum)x+Product=0\\x^{2} +12x+32=0$