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 quadratic polynomial $3 x^{2} - x - 4$ and verify the relationship between the zeroes and the coefficients.

Accepted Answer

The given polynomial is $f (x) = 3 x^{2} - x - 4$

$f (x) = 3 x^{2} - x - 4$

Splitting the middle term,

$\Rightarrow f (x) = 3 x^{2} - (4 - 3) x - 4$

$\Rightarrow f (x) = 3 x^{2} - 4 x + 3 x - 4$

$\Rightarrow f (x) = x (3 x - 4) + 1 (3 x - 4)$

$\Rightarrow f (x) = (3 x - 4) (x + 1)$

To find the zeros of the given polynomial, consider $f (x) = 0$

$\Rightarrow (3 x - 4) (x + 1) = 0$

i.e., $3 x - 4 = 0$ or $x + 1 = 0$

$\Rightarrow x = \frac{4}{3} or - 1$
Thus, zeros of the given polynomial are $\frac{4}{3}$ and $- 1$ .

Let $α = \frac{4}{3} and β = - 1$ be the two zeroes of the polynomial $f (x) = 3 x^{2} - x - 4$

We know that,

Sum of zeroes $= \frac{- Coefficient of x}{Coefficient of x^{2}} = \frac{- (- 1)}{3} = \frac{1}{3} . . . . . (i)$

And, $α + β = \frac{4}{3} - 1 = \frac{1}{3} . . . . . (i i)$

Similarly,

Product of zeroes $= \frac{Constant}{Coefficient of x^{2}} = \frac{- 4}{3} . . . . . (i i i)$

And, product of zeroes $= α β = \frac{4}{3} \times - 1 = \frac{- 4}{3} . . . . . (i v)$

Hence, from $(i), (i i)$ $&$ $(i i i), (i v)$ the relation is verified.

Find the zeroes of the quadratic polynomial $3 x^{2} - x - 4$ and verify the relationship between the zeroes and the coefficients.

Important Questions on Polynomials

Learn and Prepare for any exam you want !

Find the zeroes of the quadratic polynomial 3x2-x-4 and verify the relationship between the zeroes and the coefficients.

Important Questions on Polynomials

Learn and Prepare for any exam you want !

Find the zeroes of the quadratic polynomial $3 x^{2} - x - 4$ and verify the relationship between the zeroes and the coefficients.