Question

One of the roots of the equation 10x2−33x+c=0 is 5.3. Find the other root and the coefficient c.

Answer 1

1. The other root is
`-2`

2. c=-106

Explanation:

The given equation is
`10x^2-33x+c=0`.

If
`5.3` is a solution to the given quadratic equation, then
`x=5.3` must satisfy this equation.

`10(5.3)^2-33(5.3)+c=0`

`280.9-174.9+c=0`

`106+c=0`

`c=0-106=-106`

We now substitute
`c=-106` into the given equation to obtain;

`10x^2-33x-106=0`.

Comparing to the general equation;

`ax^2+bx+c=0`, we have a=10, b=-33 and c=-106.

Recall the quadratic formula;

`x=(-b\pm √(b^2-4ac) )/(2a)`

We now use the quadratic formula to obtain;

`x=(--33\pm √((-33)^2-4(10)(-106)) )/(2(10))`

This implies that;

`x=(33\pm √(5329) )/(20)`

`x=(33\pm73)/(20)`

`x=(33-73)/(20)` or
`x=(33+73)/(20)`

`x=(-40)/(20)` or
`x=(106)/(20)`

`x=-2` or
`x=5.3`

Hence the other root is
`-2`