Name: Division of a Trinomial by a Trinomial
Uploaded: 2019-07-19
Duration: 3 min 36 s
Description: Can we divide a polynomial by another polynomial to get the quotient polynomial and the remainder polynomial? Let's explore this concept in this video.

Question

Find the zeroes of the following quadratic polynomial and verify the relationship between the zeroes and their coefficients:

$g (s) = 4 s^{2} - 4 s + 1$ .

Accepted Answer

Given, the quadratic polynomial is $g (s) = 4 s^{2} - 4 s + 1$ .

$∴ g (s) = 4 s^{2} - 4 s + 1$

$\Rightarrow g (s) = 4 s^{2} - 2 s - 2 s + 1$

$\Rightarrow g (s) = 2 s (2 s - 1) - (2 s - 1)$

$\Rightarrow g (s) = (2 s - 1) (2 s - 1)$

The zeros of $g (s)$ are given by $g (s) = 0$ .

$g (s) = 4 s^{2} - 4 s + 1$

$\Rightarrow s = \frac{1}{2}, \frac{1}{2}$

The zeroes of the quadratic polynomial are $\frac{1}{2}$ and $\frac{1}{2}$ .

Let $α = \frac{1}{2}$ and $β = \frac{1}{2}$ .

Consider $4 s^{2} - 4 s + 1$

Sum of the zeroes $= \frac{- coefficient of s}{coefficient of s^{2}} = \frac{- (- 4)}{4} = 1 . . . (i)$

Also, $α + β = \frac{1}{2} + \frac{1}{2} = 1 . . . . (i i)$

Product of the zeroes $= \frac{constant}{coefficient of s^{2}} = \frac{1}{4} = \frac{1}{4} . . . . . . (i i i)$

Also, $α β = \frac{1}{4} . . . . (i v)$

Hence, from $(i) & (i i)$ and $(i i i) & (i v)$ the relationship between the zeroes and their coefficients is verified.

Find the zeroes of the following quadratic polynomial and verify the relationship between the zeroes and their coefficients:

$g (s) = 4 s^{2} - 4 s + 1$ .

Important Questions on Polynomials

Learn and Prepare for any exam you want !

Find the zeroes of the following quadratic polynomial and verify the relationship between the zeroes and their coefficients: g(s)=4s2-4s+1.

Important Questions on Polynomials

Learn and Prepare for any exam you want !

Find the zeroes of the following quadratic polynomial and verify the relationship between the zeroes and their coefficients:

$g (s) = 4 s^{2} - 4 s + 1$ .