Quadratic Equation

Algebra Level 3

The following Quadratic Equation have 2 roots α \alpha and β \beta :

5 x 2 + a x − 300 = 0 5{ x }^{ 2 }+ax-300=0

If α = − 12 \alpha=-12 find β + a \beta+a .


The answer is 40.

Victor Paes Plinio by Victor Paes Plinio , 21, Brazil

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1 solution

According to Viet theorem: α + β = − a 5 , α × β = − 60 , α = − 12 \alpha + \beta = -\frac{a}{5}, \alpha \times \beta = -60, \alpha = -12 ⇒ β = 5 , 5 × β + a = 60 ⇒ β + a = 40 \Rightarrow \beta = 5, 5 \times \beta+a=60 \Rightarrow \beta + a = \boxed{40}

3 Helpful 0 Interesting 0 Brilliant 0 Confused

Oh I see. I thought there was a typo, but I mixed up a a and α \alpha . You might want to consider changing the variable names...

James Wilson - 3 years, 7 months ago

Very well done sir. I was thinking of doing this.

tytan le nguyen - 6 years, 7 months ago

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