A cubic polynomial p(x) = 4x^3 - x has ...... | vedclass

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(A) To find the zeros of the polynomial $p(x) = 4x^3 - x$,we set $p(x) = 0$.$4x^3 - x = 0$Factor out $x$ from the expression:$x(4x^2 - 1) = 0$Using th

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$3$

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(A) To find the zeros of the polynomial $p(x) = 4x^3 - x$,we set $p(x) = 0$.$4x^3 - x = 0$Factor out $x$ from the expression:$x(4x^2 - 1) = 0$Using the difference of squares formula $a^2 - b^2 = (a - b)(a + b)$,we can factor $4x^2 - 1$ as $(2x - 1)(2x + 1)$:$x(2x - 1)(2x + 1) = 0$Setting each factor to zero,we get:$x = 0$,$2x - 1 = 0 \implies x = 1/2$,and $2x + 1 = 0 \implies x = -1/2$.Thus,the zeros are $0, 1/2, -1/2$.There are $3$ zeros in total.

$A$ cubic polynomial $p(x) = 4x^3 - x$ has ...... zeros.

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