Question

find the quadratic polynomial whose zeros are 1 and -3 verify the relation between the coefficient and zeros​

Answer 1

GIVEN :

The zeroes of the quadratic equation are 1 and -3

TO VERIFY:

The relation between the coefficient and zeroes

SOLUTION :

Given that the zeroes of the quadratic equation are 1 and -3

Let $\alpha=1$ and $\beta=-3$ be the zeroes of the given quadratic equation.

The quadratic equation can be written with the given zeroes is given by:

$x^2-(sum of the zeroes)x+product of the zeroes=0$

$sum of the zeroes=\alpha+\beta=1-3$

$=-2$

$sum of the zeroes=\alpha+\beta=-2$

$product of the zeroes=\alpha\times \beta=1\times (-3)$

$=-3$

$product of the zeroes=\alpha\times \beta=-3$

Then the quadratic equation can be written as

$x^2-(-2)x+(-3)=0$

$x^2+2x-3=0$ it is of the form $ax^2+bx+c=0$

Comparing the 2 equations we get the coefficients a=1 , b=2 and c=-3

The relation between the coefficient and zeroes is

$sum of the zeroes=\frac{-b}{a}$

$=\frac{-(2)}{1}$

$=-2$

∴ sum of the zeroes=-2

$product of the zeroes=\frac{c}{a}$

$=\frac{-3}{1}$

$=-3$

∴ Product of the zeroes=-3

Hence verified the relation between the coefficient and zeroes.

Answer 2

I hope it will help you all