Find the zeroes of the following polynomial $5 x^{2} - 4 - 8 x$ and verify the relationship between zeros of the polynomial and the coefficients of the polynomial.

Open in App

Solution

Step $1$ : Factorise the polynomial to find its zeroes.
$5 x^{2} - 8 x - 4 = 5 x^{2} - 10 x + 2 x - 4$
$= 5 x (x - 2) + 2 (x - 2)$
$= (x - 2) (5 x + 2) . . . . . (1)$
From equation $(1)$ we can say that the value of the given polynomial is zero when, $x = 2$ or when $x = - \frac{2}{5}$ .
Hence, the required zeroes are $2, - \frac{2}{5}$ .
Step $2$ : Verify the relationship between zeros of the polynomial and coefficients of the polynomial.
The sum of zeros $= 2 + (- \frac{2}{5})$
$= 2 - \frac{2}{5} = \frac{8}{5} = \frac{- b}{a}$
The product of zeros $= 2 \times (- \frac{2}{5})$
$= - \frac{4}{5} = \frac{c}{a}$
Hence, the zeroes of the polynomial $5 x^{2} - 4 - 8 x$ are $2, - \frac{2}{5}$ .

Suggest Corrections

Similar questions

Find the zeros of the following quadratic polynomials and verify the relationship between the zeros and the coeffients :

$5 x^{2} - 4 - 8 x$

5 x^{2} - 4 - 8 x

4 . F i n d t h e z e r o e s o f t h e p o l y n o m i a l x^{2} - x - 110 a n d v e r i f y t h e r e l a t i o n b e t w e e n t h e z e r o s a n d t h e c o e f f i c i e n t o f t h e p o l y n o m i a l .

5 . F i n d t h e z e r o e s o f t h e p o l y n o m i a l 5 x^{2} + 8 x - 4 a n d v e r i f y t h e r e l a t i o n b e t w e e n t h e z e r o s a n d t h e c o e f f i c i e n t s o f t h e p o l y n o m i a l .

Join BYJU'S Learning Program