The equation 3x 2 - 12x + (n - 5) = 0 has equal roots. Find the value of n.

Comparing 3x 2 - 12x + (n - 5) = 0 with ax 2 + bx + c = 0 we get, a = 3, b = -12 and c = (n - 5). Since equations have equal roots, ∴ D = 0 ⇒ (-12) 2 - 4.(3).(n - 5) = 0 ⇒ 144 - 12(n - 5) = 0 ⇒ 144 - 12n + 60 = 0 ⇒ 204 - 12n = 0 ⇒ 12n = 204 ⇒ n = ⇒ n = 17 Hence, n = 17.

Without solving, comment upon the nature of roots of the following equation :
25x² - 10x + 1 = 0

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Find the values of 'm', if the following equation has equal roots :
(m - 2)x² - (5 + m)x + 16 = 0

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Find the value of k for which the equation 3x² - 6x + k = 0 has distinct and real roots.

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Mathematics

The equation 3x² - 12x + (n - 5) = 0 has equal roots. Find the value of n.

Quadratic Equations

Related Questions

Without solving, comment upon the nature of roots of the following equation :
25x² - 10x + 1 = 0

Find the values of 'm', if the following equation has equal roots :
(m - 2)x² - (5 + m)x + 16 = 0

Find the value of k for which the equation 3x² - 6x + k = 0 has distinct and real roots.

Mathematics

The equation 3x2 - 12x + (n - 5) = 0 has equal roots. Find the value of n.

Quadratic Equations

Related Questions

Without solving, comment upon the nature of roots of the following equation :25x2 - 10x + 1 = 0

Find the values of 'm', if the following equation has equal roots :(m - 2)x2 - (5 + m)x + 16 = 0

Find the value of k for which the equation 3x2 - 6x + k = 0 has distinct and real roots.

The equation 3x² - 12x + (n - 5) = 0 has equal roots. Find the value of n.

Without solving, comment upon the nature of roots of the following equation :
25x² - 10x + 1 = 0

Find the values of 'm', if the following equation has equal roots :
(m - 2)x² - (5 + m)x + 16 = 0

Find the value of k for which the equation 3x² - 6x + k = 0 has distinct and real roots.