Question

Prove that the 1,-2,4 is a zeros of x3-3x2-6x+8 and verify the relationship between the zeros and their coefficient

Answer 1

Step-by-step explanation:

Given x³ - 3x² - 6x + 8.

To verify that 1 is a zero, put x = 1:

 1³ - 3×1² - 6×1 + 8  =  1 - 3 - 6 + 8  =  0.  So yes, 1 is a zero.

To verify that -2 is a zero, put x = -2:

(-2)³ - 3×(-2)² - 6×(-2) + 8  =  -8 - 12 + 12 + 8  =  0.  So yes, -2 is a zero.

To verify that 4 is a zero, put x = 4:

 4³ - 3×4² - 6×4 + 8  =  64 - 48 - 24 + 8  =  0.  So yes, 4 is a zero.

Now to verify the relationship between zeros and coefficients.

These relationships are:

• the sum of the zeros equals 3 ( minus the coefficient of x² )
• the sum of the products of the zeros, taken in pairs, equals -6 ( the coefficient of x )
• the product of the zeros equals -8 ( minus the constant coefficient ).

Verifying these one at a time:

• 1 - 2 + 4 = 3 ... yes!
• 1×(-2) + (-2)×4 + 4×1 = -2 - 8 + 4 = -6 ... yes!
• 1×(-2)×4 = -8 ... yes!

Hope this helps.