Question

Find the zero of the quadratic polynomials and verify the relationship between the zero and the coefficient :-

x² -2x -8

Answer 1

F(X)=x^2-20x+91 

comparing the equation with ax^2+bx+c=0 

a=1,=-20,c=91 

factorising this equation we get 

=x^2-13x-7x+91 

(x-13)(x-7)=0

so there are 2 factors 

first zero  :x-7=0 

second zero  x-13=0 

x=13 

x=7 

sum of zero=7+13=20 

product of zero=91 

for equaion ax^2+bx+c=0 

if zero are alpha and beta 

plug the values of a,b, c 

sum of zreos  -b/a=-(-20/1)=20 

product of zeros  c/a=91/1=91 

Answer 2

$\: \: \: \: \: \: \: \huge\colorbox{lightgreen}{αɳʂɯҽɾ ♥︎} \\ \\ \\ \\ {\sf{\pink{∴ {x}^{2} - 2x - 8 = 0 }}} \\ \: \: \: {\sf{a {x}^{2} + bx + c = 0}} \\ {\sf{∴a = 1, \: b = - 2, \: c = - 8}} \\ \\ {\sf{\pink{∴ {x}^{2} - 4x + 2x - 8 = 0 }}} \\ {\sf{↠ \: x(x - 4) + 2(x - 4) = 0}} \\ {\sf{↠ \: (x - 4)(x + 2) = 0}} \\ {\underline{\underline{\sf{\bold{\purple{∴x = 4}}}}}} \: \: \: \: {\sf{or}} \: \: \: \: {\underline{\underline{\sf{\bold{\purple{∴x = - 2}}}}}} \\ \\ \\ {\sf{\green{Verification \: ✓}}} \\ {\sf{\pink{sum \: of \: zeroes = \frac{ - b}{a} = \frac{ - ( - 2)}{1} = - 2}}} \\ \\ {\sf{\pink{product \: of \: zeroes = \frac{c}{a} = \frac{ - 8}{1} = - 8}}} \\ \\ \\ \\ {\sf{Hence, verified.}}$