What are the solutions to the equation y^2-2y-11=0 ?

The solutions to the equation y^2-2y-11=0 are y=1+2sqrt(3),y=1-2sqrt(3)

Find the zeros of y^2-2y-11=0

The zeros of y^2-2y-11=0 are y=1+2sqrt(3),y=1-2sqrt(3)

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y^{2} - 2 y - 11 = 0

y = 1 + 23, y = 1 - 23

Decimal

y = 4.46410 \dots, y = - 2.46410 \dots

Solution steps

y^{2} - 2 y - 11 = 0

Solve with the quadratic formula

y_{1, 2} = \frac{- ( - 2 ) \pm ( - 2 ) ^{2} - 4 \cdot 1 \cdot ( - 11 )}{2 \cdot 1}

(- 2)^{2} - 4 \cdot 1 \cdot (- 11) = 43

y_{1, 2} = \frac{- ( - 2 ) \pm 4 3}{2 \cdot 1}

Separate the solutions

y_{1} = \frac{- ( - 2 ) + 4 3}{2 \cdot 1}, y_{2} = \frac{- ( - 2 ) - 4 3}{2 \cdot 1}

y = \frac{- ( - 2 ) + 4 3}{2 \cdot 1} : 1 + 23

y = \frac{- ( - 2 ) - 4 3}{2 \cdot 1} : 1 - 23

The solutions to the quadratic equation are:

y = 1 + 23, y = 1 - 23

2 x^{2} + 30 = 0

16 (4 x - 1)^{2} = 25

x^{2} - 18 x + 82

x, x^{2} y^{2} + 2 x - 6 = 0

6 x^{2} - x + 6 = 0

What are the solutions to the equation y^2-2y-11=0 ?
The solutions to the equation y^2-2y-11=0 are y=1+2sqrt(3),y=1-2sqrt(3)
Find the zeros of y^2-2y-11=0
The zeros of y^2-2y-11=0 are y=1+2sqrt(3),y=1-2sqrt(3)