Question

Find about the relationship between zeroes and coefficient of a polygon with an example.

Answer 1

Dear Student,

Correction:
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Find about the relationship between zeroes and coefficient of a polynomial with an example.

Solution:
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Let us take an Quadratic polynomial,have standard equation
$a {x}^{2} + bx + c$
let zeros of equation are
$\alpha \: \: and \: \: \beta$
Sum of zeros and multiplication of zeros are given by coefficient

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

Example:

$5 {x}^{2} + 6x + 7$

is a polynomial,relation of zeros with coefficient of equation

$\alpha + \beta = \frac{ - 6}{5} \\ \\ \alpha \beta = \frac{7}{5}$
By the same way relation between cubic polynomial coefficient and zeros.

standard equation of cubic polynomial

$a {x}^{3} + b {x}^{2} + cx + d$
let
$\alpha \: \: \beta \: \: \gamma$
are the zeros of cubic polynomial

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

Hope it helps you.

Answer 2

Answer:

Let the lengths and breadth of rectangle be l & b respectively.

Now l = b+5, perimeter = 2(l+b) = 58 cm

2(b +b +5) = 58

2b + 5 = 29

2b = 24

b = 12 and length = b +5 = 17

Step-by-step explanation: