If one of the zeroes of the cubic polynomial x³ + ax² + bx + c is -1, then the product of the other two zeroes is
a. b - a + 1
b. b - a - 1
c. a - b + 1
d. a - b -1

Solution:

Given, the cubic polynomial is x³ + ax² + bx + c.

One of the zeros of the polynomial is -1.

We have to find the product of the other two zeros.

We know that, if 𝛼, ꞵ and 𝛾 are the zeroes of a cubic polynomial ax³ + bx² + cx + d, then

𝛼 + ꞵ + 𝛾 = -b/a

𝛼ꞵ + ꞵ𝛾 + 𝛾𝛼 = c/a

Where, a = coefficient of x² term

b = coefficient of x term

c = coefficient of constant term

Given, 𝛼 = -1

Here, a = 1, b = a, c = b and d = c

By the property of polynomials,

𝛼 + ꞵ + 𝛾 = -b/a

(-1) + ꞵ + 𝛾 = -a/1

(-1) + ꞵ + 𝛾 = -a

ꞵ + 𝛾 = - a + 1

𝛼ꞵ + ꞵ𝛾 + 𝛾𝛼 = b/1

(-1)ꞵ + ꞵ𝛾 + 𝛾(-1) = b

ꞵ𝛾 - ꞵ - 𝛾 = b

ꞵ𝛾 - (ꞵ + 𝛾) = b

Substituting the value of ꞵ + 𝛾,

ꞵ𝛾 - (-a + 1) = b

ꞵ𝛾 + a - 1 = b

ꞵ𝛾 = b - a + 1

Therefore, the product of the other two roots is b - a + 1

✦ Try This: If one of the zeroes of the cubic polynomial x³ + sx² + tx + u is -1, then the

product of the other two zeroes is

☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 2

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NCERT Exemplar Class 10 Maths Exercise 2.1 Problem 6

If one of the zeroes of the cubic polynomial x³ + ax² + bx + c is -1, then the product of the other two zeroes is a. b - a + 1, b. b - a - 1, c. a - b + 1, d. a - b -1

Summary:
If one of the zeroes of the cubic polynomial x³ + ax² + bx + c is -1, then the product of the other two zeroes is b - a + 1

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