What are the solutions to the equation 3pix-1.1x^2-λx=0 ?

The solutions to the equation 3pix-1.1x^2-λx=0 are x=0,x=(30pi-10λ)/(11)

Find the zeros of 3pix-1.1x^2-λx=0

The zeros of 3pix-1.1x^2-λx=0 are x=0,x=(30pi-10λ)/(11)

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3 π x - 1.1 x^{2} - λ x = 0

x = 0, x = \frac{30 π - 10 λ}{11}

Solution steps

3 π x - 1.1 x^{2} - λ x = 0

Multiply both sides by

10

30 π x - 11 x^{2} - 10 λ x = 0

Write in the standard form

a x^{2} + b x + c = 0

- 11 x^{2} + (30 π - 10 λ) x = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( 30 π - 10 λ ) \pm ( 30 π - 10 λ ) ^{2} - 4 ( - 11 ) \cdot 0}{2 ( - 11 )}

Simplify

(30 π - 10 λ)^{2} - 4 (- 11) \cdot 0 : 30 π - 10 λ

x_{1, 2} = \frac{- ( 30 π - 10 λ ) \pm ( 30 π - 10 λ )}{2 ( - 11 )}

Separate the solutions

x_{1} = \frac{- ( 30 π - 10 λ ) + 30 π - 10 λ}{2 ( - 11 )}, x_{2} = \frac{- ( 30 π - 10 λ ) - ( 30 π - 10 λ )}{2 ( - 11 )}

x = \frac{- ( 30 π - 10 λ ) + 30 π - 10 λ}{2 ( - 11 )} : 0

x = \frac{- ( 30 π - 10 λ ) - ( 30 π - 10 λ )}{2 ( - 11 )} : \frac{30 π - 10 λ}{11}

The solutions to the quadratic equation are:

x = 0, x = \frac{30 π - 10 λ}{11}

7 x - 3 x^{2} = 85 + 2 x^{2} + 2 x

3 x^{2} - 2 x = 7

x^{2} + 8 x + 43 = 0

4 y^{2} - y - 3 = 0

k^{2} = 13

What are the solutions to the equation 3pix-1.1x^2-λx=0 ?
The solutions to the equation 3pix-1.1x^2-λx=0 are x=0,x=(30pi-10λ)/(11)
Find the zeros of 3pix-1.1x^2-λx=0
The zeros of 3pix-1.1x^2-λx=0 are x=0,x=(30pi-10λ)/(11)