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