Question

Case Study -1

The figure given alongside shows the path of a diver, when she takes a jump from the diving board. Clearly it is a parabola.

Annie was standing on a diving board, 48 feet above the water level. She took a dive into the pool. Her height (in feet) above the water level at any time ‘t’ in seconds is given by the polynomial h(t) such that h(t) = -16t² + 8t + k.

A polynomial q(t) with sum of zeroes as 1 and the product as -6 is modelling Anu’s height in feet above the water at any time t( in seconds). Then q(t) is given by ______.

Options

• t² + t + 6

• t² + t - 6

• -8t² + 8t + 48

• 8t² - 8t + 48

Answer 1

A polynomial q(t) with sum of zeroes as 1 and the product as -6 is modelling Anu’s height in feet above the water at any time t( in seconds). Then q(t) is given by -8t² + 8t + 48.

Explanation:-

A polynomial q(t) with sum of zeroes as 1 and the product as -6 is given by

q(t) = k(t² - (sum of zeroes)t + product of zeroes)

= k(t² - 1t + (-6))      ...(1)

When t = 0 (initially) q(0)= 48ft

q(0)=k(0² - 1(0) - 6) = 48

i.e. -6k = 48 or k= -8

Putting k = -8 in equation (1), reqd. polynomial is -8(t² - 1t + (-6))

= -8t² + 8t + 48