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

If

α

and

β

are zeroes of the polynomial

3 x^{2} - 4 x - 7

, then form a quadratic polynomial whose zeroes are

\frac{1}{α}

and

\frac{1}{β}

.

Accepted Answer

We know that if zeros of a quadratic polynomial are $α, β$ , then, the quadratic polynomial is given by $x^{2} - (α + β) x + α β$ .

Here, given that the sum of the zeroes of the given polynomial $3 x^{2} - 4 x - 7$ is $α + β = - \frac{- 4}{3} = \frac{4}{3}$ , and the product of the zeroes is $α β = \frac{- 7}{3} = - \frac{7}{3}$ .

Now, $\frac{1}{α} + \frac{1}{β} = \frac{α + β}{α β} = \frac{\frac{4}{3}}{- \frac{7}{3}} = - \frac{4}{7}$ .

And, $\frac{1}{α} \times \frac{1}{β} = \frac{1}{α β} = \frac{1}{- \frac{7}{3}} = - \frac{3}{7}$ .

Now, all quadratic polynomials whose zeroes are $\frac{1}{α}$ and $\frac{1}{α}$ will be given by $\frac{1}{β}$ , where $k$ is any non-zero real number.

$= k [x^{2} - (- \frac{4}{7}) x + (- \frac{3}{7})]$

$= \frac{k}{7} (7 x^{2} + 4 x - 3)$

$= m (7 x^{2} + 4 x - 3)$ , where $m = 4 k$ is another non-zero real number.

Therefore, one quadratic polynomial whose zeros are $\frac{1}{α}$ and $\frac{1}{β}$ is $7 x^{2} + 4 x - 3$ .

If $α$ and $β$ are zeroes of the polynomial $3 x^{2} - 4 x - 7$ , then form a quadratic polynomial whose zeroes are $\frac{1}{α}$ and $\frac{1}{β}$ .

Important Questions on Polynomials

Learn and Prepare for any exam you want !

If α and β are zeroes of the polynomial 3x2-4x-7, then form a quadratic polynomial whose zeroes are 1α and 1β.

Important Questions on Polynomials

Learn and Prepare for any exam you want !

If $α$ and $β$ are zeroes of the polynomial $3 x^{2} - 4 x - 7$ , then form a quadratic polynomial whose zeroes are $\frac{1}{α}$ and $\frac{1}{β}$ .