Question 2 (iv)
Are the following statements ‘True’ or False’? Justify your answer.
iv) If two of the zeroes of a cubic polynomial are zero, then it does not have linear and constant terms.

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Solution

iv) True, let $α, β a n d γ$ be the zeroes of the cubic polynomial and given that two of the zeroes have value 0.
Let $β = γ = 0$
And $f (x) = (x - α) (x - β) (x - γ)$
$= (x - α) (x - 0) (x - 0)$
$= x^{3} - a x^{2}$
Which does not have linear and constant terms

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Similar questions

Q. Question 2 (v)
Are the following statements ‘True’ or False’? Justify your answer.
v) If all the zeroes of a cubic polynomial are negative, then all the coefficients and the constant term of the polynomial have the same sign.

Q. Say true or false.

If two of the zeroes of a cubic polynomial are zero, then it does not have linear and constant terms.

Question 2
Write whether the following statements are true or false. Justify your answer.

i. A Binomial can have atmost two terms.

ii. Every polynomial is a Binomial.

iii. A binomial may have degree 5.

iv. Zero of a polynomial is always 0.

v. A polynomial cannot have more than one zero.

vi. The degree of the sum of two polynomials each of degree 5 is always 5.

Q. Question 2 (vi)
Are the following statements ‘True’ or False’? Justify your answer.
vi) If all three zeroes of a cubic polynomial

x^{3} + a x^{2} - b x + c

are positive, then atleast one of a, b and c is non - negative.

Q. Question 2 (vi)
Are the following statements ‘True’ or False’? Justify your answer.
vi) If all three zeroes of a cubic polynomial

x^{3} + a x^{2} - b x + c

are positive, then atleast one of a, b and c is non - negative.

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Question 2 (iv) Are the following statements ‘True’ or False’? Justify your answer. iv) If two of the zeroes of a cubic polynomial are zero, then it does not have linear and constant terms.

iv) True, let α,β and γ be the zeroes of the cubic polynomial and given that two of the zeroes have value 0. Let β=γ=0 And f(x)=(x−α)(x−β)(x–γ) = (x−α)(x–0)(x–0) =x3–ax2 Which does not have linear and constant terms

Question 2 (iv)
Are the following statements ‘True’ or False’? Justify your answer.
iv) If two of the zeroes of a cubic polynomial are zero, then it does not have linear and constant terms.

iv) True, let $α, β a n d γ$ be the zeroes of the cubic polynomial and given that two of the zeroes have value 0.
Let $β = γ = 0$
And $f (x) = (x - α) (x - β) (x - γ)$
$= (x - α) (x - 0) (x - 0)$
$= x^{3} - a x^{2}$
Which does not have linear and constant terms