Given that the zeroes of the cubic polynomial x3-6x2+3x+10 are of the form a, a+b, q+2b, find the value of a and b as well as zeroes of the given polynomial.

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Given that the zeroes of the cubic polynomial x3-6x2+3x+10 are of the form a, a+b, q+2b, find the value of a and b as well a

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Substitute , once a,and once a+b and lastly q+2b equate to zero ,like this .a³-+a²+3a+10=0(a+b)³-6(a+b)²+3(a+b)=0and last one you will get answer .

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130

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Given Information:
The cubic polynomial is given as x^3 - 6x^2 + 3x + 10.
The zeroes of the polynomial follow a specific pattern: a, a + b, q + 2b, where a and b are unknown values.

Step 1: Finding the Value of 'a'
To find the value of 'a', we need to look at the coefficient of the x^2 term, which is -6 in this case.
According to the given pattern, the sum of the zeroes of the polynomial is equal to the opposite of the coefficient of the x^2 term.
So, a + (a + b) + (q + 2b) = -6

Simplifying the equation:
2a + 3b + q = -6

Step 2: Finding the Value of 'b'
To find the value of 'b', we need to look at the coefficient of the x term, which is 3 in this case.
According to the given pattern, the product of the zeroes taken two at a time is equal to the opposite of the coefficient of the x term.
So, a(a + b) + a(q + 2b) + (a + b)(q + 2b) = 3

Simplifying the equation:
3a^2 + 11ab + 3b^2 + aq + 2bq = 3

Step 3: Solving the Equations
Now, we have two equations with two unknowns:
2a + 3b + q = -6 ...(Equation 1)
3a^2 + 11ab + 3b^2 + aq + 2bq = 3 ...(Equation 2)

We can solve these equations simultaneously to find the values of 'a' and 'b'.

Step 4: Finding Zeroes of the Polynomial
Once we have the values of 'a' and 'b', we can substitute them back into the given pattern to find the zeroes of the polynomial.

The zeroes of the polynomial are:
a, a + b, q + 2b

Summary:
To find the values of 'a' and 'b', we solved the simultaneous equations obtained from the given pattern of zeroes. Then, we substituted the values of 'a' and 'b' back into the pattern to find the zeroes of the cubic polynomial x^3 - 6x^2 + 3x + 10.

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