Y=x^3-15x^2+72x-100.

Question

find the x and y intercepts, Show full working Please.? 

 

 

Answer 1

The equation is y = x³ - 15x² + 72x - 100.

Find the y - intercept by substituting x = 0 in the given equation.

y = 0³ - 15(0)² + 72(0) - 100

y = 0 - 0 + 0 - 100

y = - 100

The y - intercept is - 100.

Find the x - intercept by substituting y = 0 in the given equation.

0 = x³ - 15x² + 72x - 100

x³ - 15x² + 72x - 100 = 0

Graph :

The points where it crosses the x  axis  will give solutions to the polynimial function .

The graph crosses the x  - axis at a point that would suggest a factor.

It crosses the x  - axis at one point hence there are one real root.

x  = 2.4

Use synthatic division to detrmine if the given value of x  is a root of the polynomial.

Since f (2.4) = 0, x = 2.4 is a zero.

The depressed polynomial is  .

Since the depressed polynomial of this zero, , is quadratic,

use the Quadratic Formula to find the roots of the related quadratic equation

 

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The x - intercept is x = 2.4.