Name: Illustrations on Formation of Quadratic Polynomials
Uploaded: 2019-07-19
Duration: 3 min 43 s
Description: Quadratic polynomial zeros help estimate the speed of an object. In this video, let us learn how to find the quadratic polynomial using the given zeros.

Question

Find the zeroes of the following polynomials by factorisation method and verify the relations between the zeroes and the coefficients of the polynomials

$7 y^{2} - \frac{11}{3} y - \frac{2}{3}$

Accepted Answer

Let $7 y^{2} - \frac{11}{3} y - \frac{2}{3}$

$∴ 7 y^{2} - \frac{11}{3} y - \frac{2}{3}$

$\Rightarrow \frac{1}{3} (21 y^{2} - 11 y - 2)$

$\Rightarrow \frac{1}{3} (21 y^{2} - 14 y + 3 y - 2)$ [by splitting the middle term]

$\Rightarrow \frac{1}{3} (7 y (3 y - 2) + 1 (3 y - 2))$

$\Rightarrow \frac{1}{3} (3 y - 2) (7 y + 1)$

So, the value of $7 y^{2} - \frac{11}{3} y - \frac{2}{3}$ is zero when $3 y - 2 = 0$ or $7 y + 1 = 0,$

i.e., when $y = \frac{2}{3}$ or $y = - \frac{1}{7}$ .

So, the zeroes of $7 y^{2} - \frac{11}{3} y - \frac{2}{3}$ are $\frac{2}{3}$ and $- \frac{1}{7}$ .

$∴$ Sum of zeroes $= \frac{2}{3} - \frac{1}{7} = \frac{14 - 3}{21} = \frac{11}{21} = - (\frac{- 11}{3 \times 7})$

$= (- 1) . (\frac{Coefficient of y}{Coefficient of y^{2}})$

and product of zeroes $= (\frac{2}{3}) (- \frac{1}{7}) = \frac{- 2}{21} = \frac{- 2}{3 \times 7}$

$= {(- 1)}^{2} . (\frac{Constant term}{Coefficient of y^{2}})$

Hence, verified the relations between the zeroes and the coefficients of the polynomial.

Find the zeroes of the following polynomials by factorisation method and verify the relations between the zeroes and the coefficients of the polynomials

$7 y^{2} - \frac{11}{3} y - \frac{2}{3}$

Important Questions on Polynomials

Learn and Prepare for any exam you want !

Find the zeroes of the following polynomials by factorisation method and verify the relations between the zeroes and the coefficients of the polynomials 7y2-113y−23

Important Questions on Polynomials

Learn and Prepare for any exam you want !

Find the zeroes of the following polynomials by factorisation method and verify the relations between the zeroes and the coefficients of the polynomials

$7 y^{2} - \frac{11}{3} y - \frac{2}{3}$