Given that one of the zeroes of the cubic polynomial ax³ + bx² + cx + d is zero, the product of the other two zeroes is
a. -c/a
b. c/a
c. 0
d. -b/a

Solution:

Given, the cubic polynomial is ax³ + bx² + cx + d.

One of the zeros of the polynomial is zero.

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

𝛼ꞵ𝛾 = -d/a

given, 𝛼 = 0

Now, 𝛼ꞵ + ꞵ𝛾 + 𝛾𝛼 = (0)ꞵ + ꞵ𝛾 + 𝛾(0) = ꞵ𝛾

By using the property of polynomials,

ꞵ𝛾 = c/a

Therefore, the product of the other two roots is c/a.

✦ Try This: Given that one of the zeroes of the cubic polynomial rx³ + sx² + tx + u is zero, the product of the other two zeroes is

Given, the cubic polynomial is rx³ + sx² + tx + u.

One of the zeros of the polynomial is zero.

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

𝛼ꞵ𝛾 = -d/a

Where, a = coefficient of x² term

b = coefficient of x term

c = coefficient of constant term

given, 𝛼 = 0

Here, a = r, b = s, c = t, d = u

Now, 𝛼ꞵ + ꞵ𝛾 + 𝛾𝛼 = (0)ꞵ + ꞵ𝛾 + 𝛾(0) = ꞵ𝛾

By using the property of polynomials,

ꞵ𝛾 = c/a

= t/r

Therefore, the product of the other two roots is t/r

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

NCERT Exemplar Class 10 Maths Exercise 2.1 Problem 5

Summary:

Given that one of the zeroes of the cubic polynomial ax³ + bx² + cx + d is zero, the product of the other two zeroes is c/a

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