Let a,b,c be real numbers, a≠0. If a is a root of a2x2+bx+c=0,β is the root of a2x2−bx−c=0 and 0&lt;α&lt;β, then the equation a2x2+2bx+2c=0 has a root γ that always satisfies.

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fanairana7lu1

2022-04-14

Let a,b,c be real numbers,

a \neq 0

. If a is a root of

a^{2} x^{2} + b x + c = 0, β

is the root of

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

and

0 < α < β

, then the equation

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

has a root

γ

that always satisfies.

legaldaj1dn

Beginner2022-04-15Added 9 answers

You can easily find the solutions to your equations (now I choose only the correct ones):

α = \frac{- b \pm \sqrt{b^{2} - 4 a^{2} c}}{2 a^{2}}

β = \frac{- b \pm \sqrt{b^{2} + 4 a^{2} c}}{2 a^{2}}

γ = \frac{- b \pm \sqrt{b^{2} - 4 a^{2} c}}{a^{2}}

Now, if you observe the

Δ

, you can notice that are different, so possibilities A, B are incorrect because if you sum in every possible way

α

and

β

you will never obtain

γ

. But also C is incorrect because

γ \neq α

, so the right answer is D.

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