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