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Beyond Horizon Set 1 Paper 2 · Q9

Paper 2Algebra

Let a,b,ca,b,c be real numbers. Then the fourth-degree polynomial in xx:

acx4+b(a+c)x3+(a2+b2+c2)x2+b(a+c)x+acacx^4+b(a+c)x^3+(a^2+b^2+c^2)x^2+b(a+c)x+ac
Ahas four complex (non-real) roots;
Bhas either four real roots or four complex roots;
Chas two real roots and two complex roots;
Dhas four real roots.

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