What are the solutions to the equation solvefor t,0=vt+1/2 at^2 ?

The solutions to the equation solvefor t,0=vt+1/2 at^2 are t=0,t=-(2v)/a ;\quad a\ne 0

Find the zeros of solvefor t,0=vt+1/2 at^2

The zeros of solvefor t,0=vt+1/2 at^2 are t=0,t=-(2v)/a ;\quad a\ne 0

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solve for

t, 0 = v t + \frac{1}{2} a t^{2}

t = 0, t = - \frac{2 v}{a}; a \neq = 0

Solution steps

0 = v t + \frac{1}{2} a t^{2}

Multiply both sides by

2

0 = 2 t v + t^{2} a

Switch sides

2 t v + t^{2} a = 0

Write in the standard form

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

a t^{2} + 2 v t = 0

Solve with the quadratic formula

t_{1, 2} = \frac{- 2 v \pm ( 2 v ) ^{2} - 4 a \cdot 0}{2 a}

Simplify

(2 v)^{2} - 4 a \cdot 0 : 2 v

t_{1, 2} = \frac{- 2 v \pm 2 v}{2 a}; a \neq = 0

Separate the solutions

t_{1} = \frac{- 2 v + 2 v}{2 a}, t_{2} = \frac{- 2 v - 2 v}{2 a}

t = \frac{- 2 v + 2 v}{2 a} : 0

t = \frac{- 2 v - 2 v}{2 a} : - \frac{2 v}{a}

The solutions to the quadratic equation are:

t = 0, t = - \frac{2 v}{a}; a \neq = 0

c^{2} - 8 c = 0

r^{2} + 5 r = 0

s^{2} + 4 s - 60 = 0

4 x^{2} - 31 x - 45 = 0

x^{2} + 11 x = - 35

What are the solutions to the equation solvefor t,0=vt+1/2 at^2 ?
The solutions to the equation solvefor t,0=vt+1/2 at^2 are t=0,t=-(2v)/a ;\quad a\ne 0
Find the zeros of solvefor t,0=vt+1/2 at^2
The zeros of solvefor t,0=vt+1/2 at^2 are t=0,t=-(2v)/a ;\quad a\ne 0