Question

If one of the zeros of the Polynomial 3X2+8X+K is the reciprocal of the other ,then what is the value of K

Answer 1

The Given Polynomial is
$p(x) = {3x}^{2} + 8x + k$
$let \: \: \alpha \: be \: a \: zero \: of \: p(x)$
Therefore the other zero is
$\frac{1}{ \alpha }$
We know that ,

Product of zeroes = Constant term ÷ Coefficient of x^ 2

ie
$\alpha \times \frac{1}{ \alpha } = \frac{k}{3}$
ie

$k = 3$

Answer 2

Given:

The polynomial $p(x) = 3x^2 + 8x + k$.

And one of the zeroes is reciprocal of the other.

To Find:

The value of k.

Solution:

Let one of the zeroes of the given polynomial = $\alpha$

Then, another zero of the polynomial = $\frac{1}{\alpha}$

Since, general form of polynimial is $g(x) = ax^2 + bx + c$ .

So, comparing it with p(x), we get the value as following:

a = 3, b = 8 and c = k.

By the formula of product of zeroes, we have:

Product of the zeroes of a polynomial $= \dfrac{Constant \ term}{Coefficient \ of \ x^2} = \dfrac{c}{a}$

$\Rightarrow \alpha \cdot \dfrac{1}{\alpha} = \dfrac{c}{a}\\ \\\Rightarrow 1 = \dfrac{k}{3}\\\\\Rightarrow k = 3 \times 1 = 3$

Therefore, the value of k = 3.