Question

Find the quadratic polynomial of the following and verify find the coefficient of xsq-5x

Answer 1

Answer:

x^2 - 5x = 0

x^2 - 5x -0 =0

Here a=1, b=-5 and c=0

le the roots of the equation be $\alpha$ and $\beta$

$\alpha + \beta = -\frac{b}{a}$  

$\alpha$ + $\\\beta$ =- ($\frac{-5}{1}$)

$\alpha$ + $\\\beta$ = 5   ............(1)   and

$\alpha$ × $\beta$ = $\frac{c}{a}$

$\alpha$ × $\beta$ = 0/1

$\alpha$ × $\beta$ = 0      ..............(2)

now

quadraitic polynomial is in the form of:

$x^{2}$ +($\alpha$ + $\\\beta$)x +$\alpha$ × $\beta$ =0

$x^{2}$ +(-5)x + 0

$x^{2}$ -5x + 0=0

also

x^2 - 5x = 0

x(x-5) =0

x=0, (x-5) = 0

x=0, x=5

Therefore the roots of the equation are 0 and 5

let

$\alpha$ =0 then

$\beta$ =5

VERIFICATION

$\alpha$ + $\\\beta$                              $\alpha$ × $\beta$

0+5                                0 x 5

5                                      0

on cross checking eqns (1) and (2)

Hence verified

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