If \(\frac{1}{3}\) is a root of the quadratic equation x² - mx - \(\frac{10}{9}\) = 0, then value of m is:

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HPCL Engineer Civil 23 Dec 2023 Official Paper

Answer 1

Given :

x2 - mx - \(\frac{10}{9}\) = 0 and its one root = 1/3

Concept used:

If m is the root of the quadratic equation f(x), then f(m) = 0

Calculation:

f(1/3) = 0

⇒ (1/3)2 - m/3 - \(\frac{10}{9}\) = 0

⇒ 1/9 - m/3 - 10/9 = 0

⇒ -9/9 = m/3

⇒ m = -3

∴ The correct answer is -3.

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