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Answers
Step-by-step explanation:
1)
Given equation is x²+2x+1 = 0
=> (x)² +2(x)(1) + 1² = 0
=> (x+1)² = 0
=> (x+1)(x+1) = 0
=> (x+1) = 0 or (x+1) = 0
=> x = -1
The roots are -1 and -1
2)
Given equation is y²-y-2 = 0
=> y²+y-2y-2 = 0
=> y(y+1)-2(y+1) = 0
=> (y+1)(y-2) = 0
=> y+1 = 0 or y-2 = 0
=> y = -1 or y = 2
The roots are -1 and 2
3)
Given equation is x²+9x+18 = 0
=> x²+9x = -18
=> x²+2(9x)/2 = -18
=> x²+2(x)(9/2) = -18
On adding (9/2)² both sides then
=> x²+2(x)(9/2)+(9/2)² = -18+(9/2)²
=> [x+(9/2)]² = -18+(81/4)
=> [x+(9/2)]² = (-72+81)/4
=> [x+(9/2)]² = 9/4
=> x+(9/2) = ±√(9/4)
=> x+(9/2) = ±3/2
=> x = (±3/2) -(9/2)
=> x = (3/2)-(9/2) or -(3/2)-(9/2)
=> x = (3-9)/2 or (-3-9)/2
=> x = -6/2 or -12/2
=> x = -3 or -6
The roots are -3 and -6
or x²+6x+3x+18 = 0
=> x(x+6)+3(x+6) = 0
=> (x+6)(x+3) = 0
=> x+6 = 0 or x+3 = 0
=> x = -6 or x = -3
5)
Given equation is x²+5x+6 = 0
=> x²+2x+3x+6 = 0
=> x(x+2)+3(x+2) = 0
=> (x+2)(x+3) = 0
=> x+2 = 0 or x+3 = 0
=> x = -2 or x = -3
The roots are -2 and -3
6)
Given equation is 3n²-13n -10 = 0
=> 3n²+2n-15n -10 = 0
=> n(3n+2)-5(3n+2) = 0
=> (3n+2)(n-5) = 0
=> 3n+2 = 0 or n-5 = 0
=> 3n = -2 or n = 5
=> n = -2/3 or n = 5
The roots are -2/3 and 5
Step-by-step explanation:
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