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# Find the Value of M So that the Quadratic Equation Mx (X − 7) + 49 = 0 Has Two Equal Roots. - Mathematics

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ConceptQuadratic Equations Examples and Solutions

#### Question

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

#### Solution

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 = mb = −7m and c = 49

i.e., (−7m)2 − 4 × m × 49 = 0

⇒ 49m2 − 4 × × 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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Solution Find the Value of M So that the Quadratic Equation Mx (X − 7) + 49 = 0 Has Two Equal Roots. Concept: Quadratic Equations Examples and Solutions.
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