If one root of the quadratic equation 3x2 - 10x + p = 0 is \(\frac13\)

1.	If one root of the quadratic equation 3x2 - 10x + p = 0 is \(\frac13\), then the value of p and the other root respectively is :(a) 3, \(\frac13\)(b) 3, 3(c) \(-\frac13\), \(-\frac13\)(d) –3, –3
Answer» (b) 3, 3 \(\frac13\) is a root of the equation 3x² - 10x + p = 0 ⇒ 3 \(\big(\frac13\big)^2\) - 10 x \(\frac13\) + p = 0 ⇒ \(\frac13\) - \(\frac{10}{3}\) + p = 0 ⇒ \(-\frac93\) + p = 0 ⇒ p = 3 ∴ The equation becomes 3x² - 10x + 3 = 0 ⇒ 3x² - 9x - x + 3 = 0 ⇒ 3x (x - 3) - 1 (x - 3) = 0 ⇒ (3x - 1)(x - 3) = 0 ⇒ x = \(\frac13\), 3 ∴ p = 3 and the other root = 3.

If one root of the quadratic equation 3x2 - 10x + p = 0 is \(\frac13\), then the value of p and the other root respectively is :(a) 3, \(\frac13\)(b) 3, 3(c) \(-\frac13\), \(-\frac13\)(d) –3, –3

Answer»

(b) 3, 3

\(\frac13\) is a root of the equation 3x² - 10x + p = 0

⇒ 3 \(\big(\frac13\big)^2\) - 10 x \(\frac13\) + p = 0

⇒ \(\frac13\) - \(\frac{10}{3}\) + p = 0 ⇒ \(-\frac93\) + p = 0 ⇒ p = 3

∴ The equation becomes 3x² - 10x + 3 = 0

⇒ 3x² - 9x - x + 3 = 0

⇒ 3x (x - 3) - 1 (x - 3) = 0 ⇒ (3x - 1)(x - 3) = 0

⇒ x = \(\frac13\), 3

∴ p = 3 and the other root = 3.