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 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

Let the roots 𝛼 and ꞵ be zero.

Sum of the roots = 0 + 0 + 𝛾 = -b/a

b = -𝛾a

Product of two roots at a time = (0)(0) + (0)𝛾 + 𝛾(0)

0 = c/a

c = 0

So there is no linear term.

Product of all roots = (0)(0)𝛾

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.

✦ 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

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

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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

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