Question

Find the zeroes of each of the following polynomial and verify Retionship between the zeroes and their coefficients. x² - 9x+20​

Answer 1

Answer:

Step-by-step explanation:

x^2 - 5x - 4x + 20

x(x - 5) -4(x - 5)

(x-4)(x-5)

x = 4 , 5

Relationship between the zeroes and their coefficients.

quadratic equations are in form of

ax^2+bx+c

here; a = 1

b= -9

c=20

sum of the roots = -b/a

4 + 5                    =-(-9)/1

9                          = 9

product of the roots= c/a

4*5                            = 20/1

20                               =20

Answer 2

Answer:

${ \large{ \pmb{ \sf{★ Given... }}}}$

• x² - 9x + 20

${ \large{ \pmb{ \sf{★To \: Find... }}}}$

Zeroes and verifying relation between zeroes and their coefficients.

${ \large{ \pmb{ \sf{★ Solution... }}}}$

${ \implies{ \sf{ {x}^{2} - 9x + 20 = 0}}}$

$\: { \implies{ \sf{ {x}^{2} - 5x - 4x + 20 = 0}}}$

$\: { \implies{ \sf{x(x - 5) - 4(x - 5) = 0}}}$

$\: { \implies{ \sf{(x - 4)(x - 5) = 0}}}$

$\: { \implies{ \sf{x = 4 \: or \: 5}}}$

Verifying relation between zeroes and their coefficients,

Given Quadratic polynomial = x² - 9x + 20

Comparing with general form = ax² + bx + c

• ${ \sf{a = 1}}$
• $\sf{b = - 9}$
• ${ \sf{c = 20}}$

From Zeroes (4, 5)

• $\alpha = 4$
• $\beta = 5$

${ \implies{ \sf{Sum \: of \: Zeroes ( \alpha + \beta ) = \frac{ - b}{a} }}}$

$\: { \implies{ \sf{4 + 5 = \frac{ - ( - 9)}{1} }}}$

${ \implies{ \sf{9 = 9}}}$

$\: \: \:$

${ \implies{ \sf{Product \: of \: zeroes (\alpha \beta) = \frac{c}{a} }}}$

${ \implies{4 \times 5 = \frac{20}{1} }}$

${ \implies{ \sf{20 = 20}}}$

${ \large{ \pmb{ \sf{★Final \: Answer... }}}}$

Hence Verified ✔