Question

Riddhi throws a stone in the air such that it follows a parabolic path before it lands at P on the ground as depicted by the graph below.

(i) The above graph is represented by a polynomial where the sum of its zeroes is 1 and the sum of the squares of its zeroes is 25. Find the coordinates of P and Q. 

(ii) If one unit on the graph represents 25 metres, how far from Riddhi does the stone land?

Answer 1

i) Assumes the polynomial to be ax² + bx + c and considers its zeroes to be α and β. 

Given,

α + β = 1 

α² + β² = 25 

Uses the identity (α + β)² to find αβ as (-12). 

From the relation between coefficients and zeroes of a polynomial, finds b and c in terms of a as: 

b = (-a) and c = (-12a) 

Frames the expression of polynomial as: 

ax² - ax - 12a 

Assumes the value of a as 1 and factorises the above polynomial as: 

x² - x - 12 = (x - 4)(x + 3) 

Finds the zeroes as 4 and (-3). 

Thus, finds the coordinates of P and Q as (4, 0) and (-3, 0). 

ii) Writes that the distance between Riddhi and the point where the stones lands (P) is (2 + 4) = 6 units. 

Finds the distance between Riddhi and point P as (6 × 25) = 150 metres.