Question

Two friends Aryan and Om decided to go for a trekking. During summer vacation, they went to Panchmarhi. While trekking they observed that the trekking path is in the shape of a parabola. The mathematical representation of the track is shown in the graph. Based on the above information, answer the following questions. ( a ) What are the zeroes of the polynomial whose graph is given. ( b ) What will be the expression of the given polynomial p(x)? ( c ) Product of the zeroes of the polynomial which represents the parabola is____. ( d ) In the standard form of quadratic polynomial, a 2+ bx + c, a, b, and c are____.​

Answer 1

SOLUTION

TO DETERMINE

Two friends Aryan and Om decided to go for a trekking. During summer vacation, they went to Panchmarhi.

While trekking they observed that the trekking path is in the shape of a parabola. The mathematical representation of the track is shown in the graph. Based on the above information, answer the following questions.

( a ) What are the zeroes of the polynomial whose graph is given.

( b ) What will be the expression of the given polynomial p(x)

( c ) Product of the zeroes of the polynomial which represents the parabola is____.

( d ) In the standard form of quadratic polynomial, ax² + bx + c, a, b, and c are____.

EVALUATION

(a) From the graph we see that the graph of the polynomial cuts X axis at the points A( - 7,0) & B(0,10)

We know that the zeroes of a polynomial is obtained where the graph of polynomial cuts X axis

Hence zeroes of the polynomial are - 7 , 10

(b) The zeroes of the polynomial are - 7 , 10

Sum of the zeroes = - 7 + 10 = 3

Product of the Zeros = - 7 × 10 = - 70

The required polynomial

= p(x)

= $\sf{ {x}^{2} -(Sum \: of \: the \: zeroes )x + Product \: of \: the \: zeroes }$

$\sf{ = {x}^{2} - 3x - 70 }$

(c) Product of the zeroes of the polynomial

= - 7 × 10

= - 70

(d) The standard form of quadratic polynomial is given by

ax² + bx + c

Since it is a quadratic polynomial

So Coefficient of x² ≠ 0

⇒ a ≠ 0

Hence a is a non zero real number , b and c are any real numbers

━━━━━━━━━━━━━━━━

Learn more from Brainly :-

$1.$ Write the degree of the polynomial :

4z3 – 3z5 + 2z4 + z + 1

https://brainly.in/question/7735375

2. Find the degree of 2020?

https://brainly.in/question/25939171