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 quadratic polynomial

t^{2} - 15

and verify the relationship between the zeroes and the coefficients.

Accepted Answer

Given quadratic polynomial is $f (t) = t^{2} - 15$

$\Rightarrow t^{2} - {(\sqrt{15})}^{2} = (t + \sqrt{15}) (t - \sqrt{15})$

The zeroes of $f (t)$ are given by $f (t) = 0$ .

$\Rightarrow (t + \sqrt{15}) (t - \sqrt{15}) = 0$

$\Rightarrow t = - \sqrt{15}, t = \sqrt{15}$

The zeroes of the quadratic polynomial are $\sqrt{15}$ and $- \sqrt{15}$ .

Let $α = \sqrt{15}$ and $β = - \sqrt{15}$

Consider $t^{2} - 15 = t^{2} + 0 t - 15$

Sum of the zeroes $= \frac{- coefficient of t}{coefficient of t^{2}} = \frac{- (0)}{1} = 0$ … $(i)$

Also, $α + β = \sqrt{15} - \sqrt{15} = 0$ … $(i i)$

Product of the zeroes $= \frac{constant}{coefficient of t^{2}} = \frac{- 15}{1} = - 15$ … $(i i i)$

Also, $\propto β = \sqrt{15} \times - \sqrt{15} = - 15$ … $(i v)$

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 quadratic polynomial $t^{2} - 15$ 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 quadratic polynomial t2-15 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 quadratic polynomial $t^{2} - 15$ and verify the relationship between the zeroes and the coefficients.