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The quadratic equation x^2 - 2kx + (k - 1) = 0 has roots α and β such that α^2 + β^2 = 4. Without solving the equation, find the possible values of the real number k.

We know in a quadratic x^2 +bx + c = 0, -b/a = α + β and c/a = αβ. Therefore, α + β = -(-2k) = 2k, and αβ = k - 1. (Both are divided by the coefficient in front of x which is 1 so can be ignored. Now (α + β)...
RT
Answered by Ralph T. • Maths tutor
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How do I know when the subjunctive is needed in Spanish?

The Subjunctive is one of the hardest ideas in Spanish, simply because it is not commonly used in English! The easiest way I find to remember it is to think of WEIRDO! Wishes- eg when using deseo que or quie...
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Answered by Anusha P. • Spanish tutor
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Discuss the extent to which economic development in the resource-rich economies of sub-Saharan Africa is likely to be promoted by international trade

Through international trade resource-rich economies in sub-Sahara Africa will be able to increase their exports; since exports are a component of Aggregate Demand, this will increase AD. Higher AD will incre...
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Answered by Euan H. • Economics tutor
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How do you express "no matter" in Chinese?

Firstly, there are two expressions that you can use to express "no matter", these are: 1.不管 (bùguǎn) ……，都(dōu) /也 (yě)…… OR 2. 无论(wúlùn)/不论(bùlùn)……，都(dōu)/也(yě)…… The first one is more informal th...
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Answered by Lijie Y. • Mandarin tutor
6990 Views

How do I prove that the differential of coshx is equal to sinhx?

Before this proof, it is important to appreciate that both of these hyperbolic functions can be written in terms of e^x. Therefore, before you begin to differentiate, you must represent coshx as (e^x + e^-x)...
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