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 polynomial $3 z^{2} - 2 z - 1$ and verify the relation between the zeroes and its coefficients.

Accepted Answer

Given polynomial is $3 z^{2} - 2 z - 1$ .

Factorising the quadratic polynomial by splitting the middle term,

$3 z^{2} - 2 z - 1 = 3 z^{2} - 3 z + z - 1 = 3 z (z - 1) + 1 (z - 1) = (3 z + 1) (z - 1)$

To find the zeroes, the factorised form of $3 z^{2} - 2 z - 1$ should be equated zero.

$3 z^{2} - 2 z - 1$ will be zero when $3 z + 1 = 0$ or $z - 1 = 0$ .

$\Rightarrow z = \frac{- 1}{3}$ or $z = 1$ .

So, the zeroes of $3 z^{2} - 2 z - 1$ are $\frac{- 1}{3}, 1$ .

Sum of the zeroes $= \frac{- 1}{3} + 1 = \frac{2}{3}$

$\frac{- Coefficient of z}{Coefficient of z^{2}} = \frac{- (- 2)}{3} = \frac{2}{3}$

$\Rightarrow$ Sum of zeroes $= \frac{- Coefficient of z}{Coefficient of z^{2}} = \frac{2}{3}$

Product of zeroes $= (\frac{- 1}{3}) \times (1) = \frac{- 1}{3}$

$\frac{Constant term}{Coefficient of z^{2}} = \frac{- 1}{3}$

$\Rightarrow$ Product of zeroes $= \frac{Constant term}{Coefficient of z^{2}} = \frac{- 1}{3}$

Hence, verified.

Find the zeroes of the polynomial $3 z^{2} - 2 z - 1$ and verify the relation between the zeroes and its coefficients.

Important Questions on Polynomials

Learn and Prepare for any exam you want !

Find the zeroes of the polynomial 3z2-2z-1 and verify the relation between the zeroes and its coefficients.

Important Questions on Polynomials

Learn and Prepare for any exam you want !

Find the zeroes of the polynomial $3 z^{2} - 2 z - 1$ and verify the relation between the zeroes and its coefficients.