If one of the zeroes of cubic polynomial X3 ax2 bx c is -1 then the product of other 2zetoes?

Question

Answer

If there is + sign between whole eqn. then answer may be c product of zeroes = -d / a alpha = -1 alpha × beeta × gama = -d / a - 1 × beeta × gaama = - d/ a beeta × gama =  - c / -1 beeta × gama = c Product of two zeroes = c

Answer

Explanation:

Let the zeroes of the polynomial be -1, α and β.

According to the factor theorem, a polynomial with zeroes α and β can be written as:

x² + (α + β)x + αβ

As the polynomial has -1 as one of its zeroes, it can be written as:

x + 1

Now, equating the two expressions for the polynomial, we get:

x + 1 = x² + (α + β)x + αβ

Comparing the coefficients of x², x and the constant term, we get:

α + β = 0

αβ = -1

Now, we need to find the product of the other two zeroes α and β.

Solution:

From the equation α + β = 0, we get:

β = -α

Substituting this in the equation αβ = -1, we get:

α(-α) = -1

-α² = -1

α² = 1

α = 1 or α = -1

Since we already know that one of the zeroes is -1, the other two zeroes can be:

α = 1 and β = -1

or

α = -1 and β = 1

Therefore, the product of the other two zeroes is:

αβ = (1)(-1) = -1

or

αβ = (-1)(1) = -1

Hence, the product of the other two zeroes of the cubic polynomial is -1.

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