Question

A quadratic polynomial, whose sum of zeroes is 0 and one zero is 3..is..????

Answer 1

Answer:

Let α  and β are the zeroes of the polynomial.

Given : Sum of the zeroes (α + β) = 0 and one zero (α) = 3 .

(α + β) = 0 ………………..(1)

3 + β = 0

β = 0 - 3

β = - 3

On substituting β = - 3 in eq 1 .

(α + β) = 0

α +(-3 )= 0

α - 3 = 0

α = 3  

Product of the zeroes = αβ

Product of the zeroes = 3 × -3 = -9

αβ = - 9 ………………(2)

Then, the required quadratic polynomial is :  

[x² –(sum of the zeroes)x + (product of the zeroes)] = 0  

= [x² –(α + β)x + (α β)]  

= x² -(0)x + (-9)

[From eq 1 & 2 ]

= x² - 9

Hence, the required quadratic polynomial is x² - 9.

Answer 2

Step-by-step explanation:

GIVEN :-

$\alpha + \beta = 0$

$\alpha = 3$

Then ,

$\beta = - 3$

Now a quadratic equation is of the form

$x {}^{2} - x( \alpha + \beta ) + \alpha \beta$

so, the equation is

$x {}^{2} - 9$

Hope it helps

$<marquee><h1><font color = purple> prabhudutt$