plz... can you help me frndz??? plz do the middle term splitting....!
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firstly multiple the first term to the second term
than see that
the number which is multipled ex-
x.2 it will 2 and the middle term is X it will
2-1
(1) 6x^2 -x -1
6x^2 + 2x -3x -1 = 0
2x( 3x + 1) - 1(3x + 1) = 0
(2x - 1)(3x+ 1) = 0
》 2x - 1 = 0
2x = 1
x = 1/2
》 3x +1 = 0
3x = -1
x = -1/3
Verifying the relationship between zeroes and coefficients.
sum of the zeroes = - b/a
1/2 + (- 1/3) = -(-1)/6
1/2 - 1/3 = 1/6
3-2/6 = 1/6
1/6 = 1/6
LHS = RHS
product of the zeroes = c/a
1/2 × -1/3 = -1/6
-1/6 = -1/6
LHS = RHS
•°•The relationship between zeroes and coefficients is verified.
====================
(2) 25x (x + 1) + 4
25x^2 + 25x + 4 =0
25x^2 + 5x + 20x + 4 =0
5x( 5x + 1)+4 ( 5x +1)=0
(5x + 4 )(5x + 1) = 0
》 5x + 4 = 0
5X = -4
X = -4/5
》 5x + 1 = 0
5x = - 1
x = -1/5
Verifying the relationship between zeroes and coefficients.
sum of the zeroes = -b/a
-4/5 + (-1/5) = -25/25
-4/5 -1/5 = -25/25
-20-5/25= -1
-25/25 = -1
-1 = -1
LHS= RHS
product of zeroes = c/a
-4/5 × (-1/5)= 4/25
4/25 = 4/25
LHS = RHS
•°•The relationship between zeroes and coefficients is verified.
====================
(3) 4x^2 + 4x + 1
4x^2 + 2x + 2x + 1 = 0
2x ( 2x + 1)+1 (2x + 1) =0
(2x + 1)(2x +1)=0
》2x = -1
x = -1/2
(in both cases the answer is same )
Verifying the relationship between zeroes and coefficients.
sum of the zeroes = -b/a
-1/2 + (-1/2) = -4/4
-1/2 -1/2 = -1
-2-2/4 = -1
-4/4 = -1
-1 = -1
LHS= RHS
product of zeroes = c/a
-1/2 × (-1/2) = 1/4
1/4 = 1/4
LHS = RHS
•°•The relationship between zeroes and coefficients is verified.
====================
(4) 48y^2 - 13y -1=0
48y^2 + 3y -16y -1=0
3y (16y + 1) -1 (16y +1) =0
(3y -1)(16y+1) = 0
》3y -1 =0
3y = 1
y = 1/3
》16y +1 =0
16y = -1
y = -1/16
Verifying the relationship between zeroes and coefficients.
sum of the zeroes = - b / a
1/3 + (-1/16) = -(-13/48)
16-3/48 = 13/48
13/48 = 13/48
LHS = RHS
product of the zeroes = c / a
1/3 × (-1/16) = -1/48
-1/48 = -1/48
LHS = RHS
•°•The relationship between zeroes and coefficients is verified.
===================
(5) 63 -2x -x^2
x^2 +2x -63 = 0
x^2 +9x -7x-63 =0
x (x + 9) -7 (x+9) = 0
( x-7)(x+9) = 0
》 x-7 = 0
X = 7
》x+9 =0
X = - 9
Verifying the relationship between zeroes and coefficients.
sum of the zeroes = - b / a
7+(-9) = -2/1
-2 = -2
LHS = RHS
product of the zeroes = c / a
7× (-9) = -63/1
-63 = - 63
LHS = RHS
•°•The relationship between zeroes and coefficients is verified.
====================
(6) 2x^2 - 5x = 0
X(2x -5) = 0
》x = 0
》2x - 5 = 0
2x = 5
x = 5/2
Verifying the relationship between zeroes and coefficients.
sum of the zeroes = - b / a
0 + 5/2 = -(-5/2)
5/2 = 5/2
LHS = RHS
product of the zeroes = c / a
0 × 5/2 = 0/5
( °•° 'c' term is absent so we take it as zero)
0 = 0
LHS = RHS
•°•The relationship between zeroes and coefficients is verified.
================
(7) 49x^2 - 81 =0
49x^2 = 81
x^2 = 81/49
x = under root 81/49
x = +-9/7
The two zeroes are +9/7 and -9/7
Verifying the relationship between zeroes and coefficients.
sum of the zeroes = - b / a
9/7 + (-9/7) = -0/49
0=0
LHS = RHS
product of the zeroes = c / a
9/7 × -9/7 = -81/49
-81/49 = -81/49
LHS = RHS
•°•The relationship between zeroes and coefficients is verified.
======================
(8) 4x^2 -4x -3 =0
4x^2 +2x -6x-3 =0
2x ( 2x + 1)-3 (2x+1) =0
(2x - 3)(2x + 1 ) = 0
》2x -3=0
x = 3/2
》2x + 1 = 0
x = -1/2
Verifying the relationship between zeroes and coefficients
sum of the zeroes = - b / a
3/2 +(-1/2) =-(-4)/4
2/2 = 1
1=1
LHS = RHS
product of the zeroes = c / a
3/2 × (-1/2) = -3/4
-3/4 = -3/4
LHS = RHS
•°•The relationship between zeroes and coefficients is verified.