Question

Explain the Relationship between Zeroes and coefficient of quadratic polynomials .

Answer 1

Consider a qaudratic polynomial f(x)=ax2+bx+c. The coeffients of this polynomial are a,b and c.

Let its zeroes be α and β. We can write [ math]ax^2+bx+c = a(x-\alpha)(x-\beta)[/math]

or ax2+bx+c=ax2−a(α+β)x+aαβ

Comparing the coefficient of each term on both sides, we have

b=−a(α+β)

or α+β=−ba

and

c=aαβ  

or αβ=ca

Answer 2

a=1.

$\alpha = 1 \: \: \beta = - 1 \: \: \: \gamma = - 3$

b=3

c=-1

d=-3

..........

$\alpha + \beta + \gamma = - \frac{ - b}{a}$

1+(-1)+(-3)=1 -1 -3=-3

$\frac{ - b}{a } = - 3$

$\alpha \beta + \beta \gamma + \gamma \alpha = \frac{c}{a}$

1(-1)+(-1)(-3)+(-3)1=-1+3-3

=1

c/a=-1

$\alpha \beta \gamma = \frac{ - d}{a}$

(1)(-1)(-3)=3

-d/a=-(-3)/1

=3

hope this will help u ✌️☺️✔️ and this is one example^_^❤️⏪