1.) x² + 6x + 9 = 0

a = 1

b = 6

c = 9

b² - 4ac

(6)²- 4(1)(9)

36-36

Discriminant= 0

Nature of roots: real and equal :)

Answer:

1) x² + 6x + 9 = 0 x=-3 and x=-3

2) x² + 6x + 8 = 0 x=-2 and x=-4

3) 2x² + 5x + 7 = 0  x=-5+√-31/4 and x=-5-√-31/4

4) 3x² + 10x + 2 =c x=-10+√76/6 and x=-10-√76/6

Solution:

#USING ANY METHODS OF A QUADRATIC EQUATION

1) x² + 6x + 9 = 0

#USING BY FACTORING

(x+3) (x+3)=0

x²+3x+3x+9=0 (FOIL METHOD)

x²+6x+9=0

(x+3) (x+3)=0

(x+3)=0 (x+3)=0

x=-3 and x=-3

#The roots of x²+6x+9=0 are x=-3 and x=-3#

2) x² + 6x + 8 = 0

#USING BY FACTORING

(x+2) (x+4)=0

x²+4x+2x+8x=0

x²+6x+8=0

(x+2) (x+4)=0

(x+2)=0 (x+4)=0

x=-2 and x=-4

#The roots of x²+6x+8=0 are x=-2 and x=-4#

3) 2x² + 5x + 7 = 0

#USING QUADRATIC FORMULA

a=2 b=5 c=7

x=-b±√b²-4ac/2a

x=-5±√(5)²-4(2)(7)/2(2)

x=-5±√(25)-56/4

x=-5±√-31/4

x=-5+√-31/4 and x=-5-√-31/4

#The roots of 2x²+5x+7=0 are x=-5+√-31/4 and x=-5-√-31/4#

4) 3x² + 10x + 2=c

#USING QUADRATIC FORMULA

a=3 b=10 c=2

x=-b±√b²-4ac/2a

x=-10±√(10)²-4(3)(2)/2(3)

x=-10±√(100)-(24)/6

x=-10±√76/6

x=-10+√76/6 and x=-10-√76/6

#The roots of 3x²+10x+2=c are x=-10+√76/6 and x=-10-√76/6#

#LEARNING IS FUN

#STUDY HARD

#CARRY-ON-LEARNING