Question

solve these for 25 points!!!!!
xplain them properly pls

Answer 1

hi friend !
a)       x²-2x-8=0
    x²-4x+2x-8=0
    x(x-4)+2(x-4)=0
    (x-4)(x+2)=0
x=4 or -2
relation between coefficients is
sum of zeros = -b/a
               4-2 = +2
product of zeros = c/a
          4X (-2)     = -8
Hence verified
______________________________________________________________
b)        4s²-4s+1  =0
        4s²-2s-2s+1=0
  2s(2s-1)-1(2s-1)=0
         (2s-1)(2s-1)=0
so x= 1/2 or x= 1/2
relation;- sum = 1/2+1/2= -b/a=+4/4=1
              product =1/4= c/a1/4
Hence verified
_____________________________________________________________
c)            6x²+7x-3=0
          6x²+9x-2x-3=0
  3x(2x+3)-1(2x+3)=0
          (2x+3)(3x-1)=0
x=-3/2 or x= 1/3
sum of zeros = -9/6=-b/a=-9/6
product of zeros= -1/2= c/a=-1/2
Hence verified
____________________________________________________________
d) 4u²+8u=0
    4u(u+2)=0
 u=0 and u=-2
 sum of zeros = -2=-b/a=-2
product of zeros = 2x0=0=c/a= 0
Hence verified
_____________________________________________________________
e) t²-15=0
    t²=15
    t =√15
 t = -√15 or +√15
so sum of zeros = 0 = -b/a=0
product of zeros = -15=c/a= -15
 Hence verified
_____________________________________________________________
f) 3x²-x-4=0
   3x²-4x+3x-4=0
   x(3x-4)+1(3x-4)=0
  (3x-4)(x+1)       = 0
 x= 4/3 or x= -1
so, sum of zeros = -1/3= -b/a= -1/3
     product of zeros=-4/3=c/a=-4/3
Hence verified
_________________________________________________________________________________________________________Hope you like it :)_____

Answer 2

a) x² -2x -8 = 0
x² -4x +2x -8 =0
x( x -4) +2 ( x -4) =0
( x -4)( x +2) =0
x = 4, -2

now,
sum of roots = -b/a = -(-2/1) = 2
sum of roots = 4 + (-2) = 2

products of roots = c/a = -8/1 = -8
products of roots = (4)(-2) = -8


b) 4s² -4s + 1 =0
(2s)² -2(2s).1 +(1)² =0
(2s -1)²=0
s = 1/2 , 1/2
sum of roots = -b/a = -(-4)/(4) = 1
sum of roots = 1/2 + 1/2 = 1

products of roots = c/a = 1/4
products of roots =(1/2)(1/2) =1/4


c) 6x² -3 +7x =0
6x² +7x -3 =0
6x² +9x -2x -3 =0
3x (2x +3)-(2x +3)=0
(3x -1)(2x +3)=0
x =1/3 , -3/2

sum of roots = -b/a = -(7/6) = -7/6
sum of roots = -3/2 + 1/3 = -7/6

products of roots = c/a = -3/6 = -1/2
products of roots =(1/3)(-3/2) = -1/2


d) 4u² + 8u =0
4u( u +2) =0
u = 0, -2
sum of roots = -b/a = -(8)/(4) = -2
sum of roots = 0 +(-2) = -2

product of roots = c/a = 0/4 = 0
product of roots = 0×(-2) = 0

e) t² -15 =0
(t -√15)(t+√15) =0
t = √15 , -√15
sum of roots = -b/a = -(0)/1 =0
sum of roots = √15 -√15 = 0

product of roots = c/a = (-15)/1 = -15
product of roots = (√15)(-√15) = -15

f) 3x² -x -4 =0
3x² -4x +3x -4 =0
3x² +3x -4x -4 =0
3x(x + 1)) -4(x +1) =0
(3x -4)(x + 1) =0
x = 4/3 , -1

sum of roots = -b/a = -(-1)/3 = 1/3
sum of roots = 4/3 -1 = 1/3

product of roots = c/a = (-4)/3 = -4/3
product of roots = (4/3)(-1) = -4/3