Question

Find the value of m so that the quadratic equation mx (x − 7) + 49 = 0 has two equal roots.

Answer 1

The given quadratic equation i.e., mx (x − 7) + 49 = 0 can be rewritten as follows: 

mx (x − 7) + 49 = 0 

⇒ mx² − 7mx + 49 = 0 

Since the given quadratic equation has equal roots, its discriminant is 0. 

i.e., b² − 4ac = 0, where a = m, b = −7m and c = 49

i.e., (−7m)² − 4 × m × 49 = 0

⇒ 49m² − 4 × m × 49 = 0

⇒ 49m (m − 4) = 0

⇒ m = 0 or m − 4 = 0

⇒ m = 0 or m = 4

∴ m = 4 (∴m ≠ 0)

Thus, the value of m is 4