Express r1^2 + r2^2 for a quadratic ax^2… | Answer | TuitionWave

Subject

গণিত

Topic

Algebra

Express r1^2 + r2^2 for a quadratic ax^2 + bx + c = 0 in terms of coefficients.
Reading

ক)

(−b/a)^2 − 2(c/a)

খ)

(b/a)^2 + 2(c/a)

গ)

2(−b/a) − (c/a)

ঘ)

(−b/a)^2 + 2(c/a)

Explanation

Start with Viète's relations for the quadratic ax^2 + bx + c = 0: r1 + r2 = −b/a, r1 r2 = c/a. Compute

r_1^2 + r_2^2 = (r_1 + r_2)^2 - 2r_1r_2 = \Big(\!-\frac{b}{a}\!\Big)^2 - 2\cdot\frac{c}{a} = \frac{b^2}{a^2} - \frac{2c}{a} = \frac{b^2 - 2ac}{a^2}.

Thus the correct choice is Option 1:

\displaystyle \Big(-\frac{b}{a}\Big)^2 - 2\frac{c}{a}.

(Option 4, which has a plus sign, is incorrect.)

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