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Black Advanced Problems in Mathematics
Exam
Black Advanced Problems in Mathematics
Subject
Mathematics
Chapter
Quadratic Equation

Black Advanced Problems in Mathematics · Mathematics · Quadratic Equation

If α and β are the roots of the equation ax^2 + bx + c = 0; a, b, c...

If α\alpha and β\beta are the roots of the equation ax2+bx+c=0;a,b,c∈R;a≠0ax^2 + bx + c = 0; a, b, c \in \mathbb{R}; a \ne 0 then which is (are) correct:

Options

  1. Aα2+β2=b2−2aca2\alpha^2 + \beta^2 = \frac{b^2 - 2ac}{a^2}
  2. B1α2+1β2=b2−2acc2\frac{1}{\alpha^2} + \frac{1}{\beta^2} = \frac{b^2 - 2ac}{c^2}
  3. C1α3+1β3=abc−b3c3\frac{1}{\alpha^3} + \frac{1}{\beta^3} = \frac{abc - b^3}{c^3}
  4. Dαβ(α+β)=−bca2\alpha\beta(\alpha+\beta) = -\frac{bc}{a^2}.

Correct answer

A. α2+β2=b2−2aca2\alpha^2 + \beta^2 = \frac{b^2 - 2ac}{a^2}

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