If two of the zeroes of a cubic polynomial are zero, then it does not have linear and constant terms. Is the statement true or false? Justify your answer
Solution:
Given, two zeros of a cubic polynomial are zero.
We know that, if ๐ผ, ๊ต and ๐พ are the zeroes of a cubic polynomial ax³ + bx² + cx + d, then
๐ผ + ๊ต + ๐พ = -b/a
๐ผ๊ต + ๊ต๐พ + ๐พ๐ผ = c/a
๐ผ๊ต๐พ = -d/a
Let the roots ๐ผ and ๊ต be zero.
Sum of the roots = 0 + 0 + ๐พ = -b/a
b = -๐พa
Product of two roots at a time = (0)(0) + (0)๐พ + ๐พ(0)
0 = c/a
c = 0
So there is no linear term.
Product of all roots = (0)(0)๐พ
0 = -d/a
d = 0
So there is no constant term.
The polynomial becomes ax³ + bx².
Therefore, the polynomial has no linear and constant term.
โฆ Try This: If two of the zeroes of a cubic polynomial 4x³ + 2x² + x + 3 are zero, then it does not have linear and constant terms. Is the statement true or false? Justify your answer
โ Also Check: NCERT Solutions for Class 10 Maths Chapter 2
NCERT Exemplar Class 10 Maths Exercise 2.2 Problem 2 (iv)
If two of the zeroes of a cubic polynomial are zero, then it does not have linear and constant terms. Is the statement true or false? Justify your answer
Summary:
If two of the zeroes of a cubic polynomial are zero, then it does not have linear and constant terms.The statement is true
โ Related Questions:
- If all three zeros of a cubic polynomial x³ + ax² - bx + c are positive, then at least one of a, b a . . . .
- The only value of k for which the quadratic polynomial kx² + x + k has equal zeros is 1/2. Is the st . . . .
- Find the zeroes of the polynomial x² + (1/6)x - 2, and verify the relation between the coefficients . . . .