Question

Find the condition that the zeros of the polynomial x cube minus 3 X square + 2 x minus are in arithmetic progression.​

Answer 1

Answer:

-1 is to be added to fulfil the condition.

Step-by-step explanation:

Polynomial = $x^{3}$ - 3$x^{2}$ + 2$x$ - 0

Let's add -1 to the polynomial = $x^{3}$ - 3$x^{2}$ + 2$x$ - 0 + (-1)

                                                 =  $x^{3}$ - 3$x^{2}$ + 2$x$ - 1

Zeros of the Polynomial;

• α + β + γ = $\frac{-b}{a}$ = $\frac{-(-3)}{1}$ = 3

• αβ + βγ + γα = $\frac{c}{a}$ = $\frac{2}{1}$ = 2
• αβγ = $\frac{-d}{a}$ = $\frac{-(-1)}{1}$ = 1

Zeros are in A.P. with a(1st Term)= 3 and d(Common Difference)= 1

• a=3
• a-d=2
• $a_{2}$-d=1

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