Question

$\Large{\tt{Question:}}$

✯ Given that the equation 12x³ -4x² - 5x + 2 has two zeroes equal, find all the zeroes.

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Answer 1

Answer:

x = 1/2 ,1/2 ,-3/2

Step-by-step explanation:

Given

12x³ -4x² - 5x + 2

• two zero equals of above polynomial

Now

p(x)= 12x^3 - 4 x^2 - 5x + 2

on putting x = 0

p(x) = 2

on putting x = 1/2

p(x ) = 0

so

one zeros is 1/2

on dividing (x - 1/2) we get

12x^2 + 2x - 4 = 0

6x^2 + x - 2= 0

6x^2 +4x -3x - 2 = 0

2x(3x +2) - ( 3x +2) = 0

(2x -1)(3x +2) = 0

so

x = 1/2 and -2/3

so 3 zero of polynomial is -2/3 ,1/2 and 1/2

Answer 2

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f(x)=x3−12x2+19x−28

Zeroes are in AP.

Let the zeroes be of the form

a-d,a,a+d

sum of roots = 12

3a=12

a = 4

product of roots =−ad

a(a2−d2)=(−28)

a3−ad2=28

(4)3−4d2=28

64−4d2=28

4d2=36

d=±3

Zeroes are 1,4,7 or 7,4,1  

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