Question

QUADRATIC EQUATIONS
A) Solve the quadratic equations.
1)
${n }^{2} - n \: - 20 = 0$
2)
${x}^{2} - 2x \: - 8 = 0$
3)
$x(x + 4) = 12$
4)
$x - \frac{3}{x } = 2$
5)
$x + \frac{3}{x} = 2$
6)
$\sqrt{2 {x}^{2} } + 7x + 5 \sqrt{2} = 0$
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Answer 1

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Answer:

• n^2-n-20=0

n^2+4n-5n-20=0

n(n+4)-5(n+4)=0

(n-5)(n+4)=0

n=5,-4

• x^2-2x-8=0

x^2+2x-4x-8=0

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

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

x=4,-2

• x(x+4)=12

x^2+4x-12=0

x^2-2x+6x-12=0

x(x-2)+6(x-2)=0

(x+6)(x-2)=0

x=2,-6

• x-3/x=2

(x^2-3)/x=2

x^2-2x-3=2

x^2+x-3x-3=0

x(x+1)-3(x+1)=0

(x-3)(x+1)=0

x=3,1

• x+3/x=2

x^2-2x+3=0

x= -b±√(b^2-4ac)/2a

x= -(-2)±√{(-2)^2-4(1)(3)}/2(1)

x=2±√(4-12)/2

x=2±√-8/2