Given that two of the zeroes of the cubic polynomial ax 3 bx² cx d are 0 the third zero is 1 point

Last updated at Dec. 4, 2021 by Teachoo

This video is only available for Teachoo black users

Support Teachoo in making more (and better content) - Monthly, 6 monthly, yearly packs available!

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

Two zeros of the polynomial are zero.

We have to find the third zero of the polynomial.

Let first zero be 𝛼, so 𝛼 = 0

Let second zero be ꞵ, so ꞵ = 0

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

Sum of the roots is 𝛼 + ꞵ + 𝛾 = -b/a

By the property, 0 + 0 + 𝛾 = -b/a

Therefore, the third zero is -b/a.

✦ Try This: Given that two of the zeroes of the cubic polynomial rx³ + sx² + tx + u are 0, the third zero is

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

Two zeros of the polynomial are zero

We have to find the third zero of the polynomial.

Let first zero be 𝛼, so 𝛼 = 0

Let second zero be ꞵ, so ꞵ = 0

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

Sum of the roots is 𝛼 + ꞵ + 𝛾 = -b/a

Here, a = r and b = s

By the property, 0 + 0 + 𝛾 = -b/a

𝛾 = -s/r

Therefore, the third zero is -s/r

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

NCERT Exemplar Class 10 Maths Exercise 2.1 Solved Problem 2

Summary:

Given that the two zeros of the cubic polynomial ax³ + bx² + cx + d are zero, the third zero is -b/a

☛ Related Questions:

• A quadratic polynomial, whose zeroes are -3 and 4, is, a. x2 - x + 12, b. x2 + x + 12, c. x² /2 - x . . . .
• If the zeroes of the quadratic polynomial x² + (a + 1) x + b are 2 and -3, then a = -7, b = -1, a = . . . .
• The number of polynomials having zeroes as -2 and 5 is, a. 1, b. 2, c. 3, d. more than 3