Class 10 Math All topics Polynomials

Say true or false.

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

(a)

True

(b)

False

Correct answer: (a)

Solution: True.

Let the general cubic polynomial be $ax_{3}+bx_{2}+cx+d=0$ and $α,β$ and $γ$ are roots of the polynomial

Linear term of polynomial implies to the coefficient of $x$, ($c$ in the above equation), and the constant term implies to the term independent of $x$, ($d$ in above equation).

Given, two zeroes of the cubic polynomial are zero. Let two zeros ie.,$β,γ$ =0.

Let the general cubic polynomial be $ax_{3}+bx_{2}+cx+d=0$ and $α,β$ and $γ$ are roots of the polynomial

Linear term of polynomial implies to the coefficient of $x$, ($c$ in the above equation), and the constant term implies to the term independent of $x$, ($d$ in above equation).

Given, two zeroes of the cubic polynomial are zero. Let two zeros ie.,$β,γ$ =0.

$f(x)=(x−α)(x−β)(x−γ)$

$f(x)=(x−α)(x−0)(x−0)$

$f(x)=(x−α)(x_{2})$

$(f(x)=(x_{3}−x_{2}α)$

then the equation does not have linear term (coefficient of $x$ is $0$) and constant term.

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