Question

Find the value of ‘m’ for which the following
equation has equal roots
(m – 12)x
2
+ 2(m – 12)x + 2 = 0​

Answer 1

Given:

An equaation (m – 12)x 2 + 2(m – 12)x + 2 = 0​

To find:

Find the value of ‘m’ for which the following  equation has equal roots (m – 12)x² + 2(m – 12)x + 2 = 0​

Solution:

From given, we have,

The condition for a quadratic equation to have equal roots is,

b² - 4ac = 0

for given quadratic equation, (m – 12)x ² + 2(m – 12)x + 2 = 0​

a = m - 12

b = m - 12

c = 2

substitute the values in the condition,

b² - 4ac = 0

(m - 12)² - 4 (m - 12) (2) = 0

m² + 144 - 24m - 8m + 96 = 0

m² - 32m + 240 = 0

(m - 12) (m - 20) = 0

m = 12, 20

Therefore, the value of ‘m’ for which the following  equation has equal roots (m – 12)x² + 2(m – 12)x + 2 = 0​ is 12 and 20.