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.

Top Courses for Class 10View all

Science Class 10

Social Studies (SST) Class 10

Mathematics (Maths) Class 10

English Grammar Advanced

English Grammar Basic

Top Courses for Class 10

Top Courses for Class 10

Suggested Free Tests

Related Content

About Class 10

Class 10 Study Material

Class 10 All Subjects

NCERT Textbook Solutions

Other Classes

Important Links

Company