Question

if the path traced by the car has zeros at -1 and 2,then it is given by the equation is

Answer 1

Given: The path traced by cars has zeroes -1 and 2.

To find: Equation of the path

Solution: Since the given path has two roots, therefore the path is in the form of a quadratic equation.

Let the roots be denoted by a and b.

a= -1 and b =2

Sum of the roots

= -1 +2

= 1

Product of roots

= -1 × 2

= -2

A quadratic equation is written as:

${x}^{2} - (sum \: of \: roots)x + product \: of \: roots = 0$

$= > {x}^{2} - 1x + ( - 2) = 0$

$= > {x}^{2} - x - 2 = 0$

Therefore, the equation of the path is ${x}^{2} - x - 2 = 0$.