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

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(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

Vedclass · Accepted Answer

$3$

Vedclass · Answer

(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.

Similar Questions

Verify that the numbers given alongside the cubic polynomials below are their zeroes. Also,verify the relationship between the zeroes and the coefficients in each case: $x^{3}-4x^{2}+5x-2; 2, 1, 1$.

State the degree of the given polynomial: $p(x) = x^{2} - \sqrt{3}x^{3} + 4x^{7} + 9$.

The sum of the zeros of $p(x) = 4x^2 + 12x + 5$ is.........

The zeros of the quadratic polynomial $p(x) = x^{2} - 3x + 2$ are $\alpha$ and $\beta$. Then,$\frac{1}{\alpha} + \frac{1}{\beta} = \ldots$

Verify that $\frac{-2}{3}$ is a zero of the linear polynomial $p(x)=3x+2$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module