N or Y Q.40 Q.50 page 636
The third letter of my last name is N so I have to do the above two problems
Quadratic formula
Factoring
Completing the square
Discriminant
Q.40 solve by completing the square
3x2 – 6x = 24
Dividing all terms by 3
x2 – 2x = 12
middle term is -2 we half it and then add its square to complete the square on left side
-2 /2 = -1 and ( -1)2 = 1
Adding 1 to both sides
x2 – 2x + 1 = 12 + 1
(x – 1)2 = 13
Taking square root of both sides
x - 1 = ± √13
x = 1 ± √13
x = 1 + √13 , 1 - √13
q.50 x2 + 10x – 3 = 0
the quadratic formula is
x = -b ± √ D
2a
D is the discriminant, D = b2 – 4ac
If D > 0 we get real roots,
D = 0 we get equal roots
D < 0 we get imaginary roots
Here a = 1, b = 10, c = -3
D = 102 – 4*1*-3 = 100 + 12 = 112
x = -10 ± √ 112
2*1
x = -10 ± √4*4*7
2
x = -10 ± 4 √7
2
x = -5 ± √7
x = -5 + √7, -5 - √7
