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प्रश्न
If quadratic equation x2 − (m + 1) x + 6 = 0 has one root as x = 3; find the value of m and the root of the equation.
उत्तर
x2 − (m + 1) x + 6 = 0
Step 1: Substitute x = 3 into the equation
32 − (m + 1) (3) + 6 = 0
9 − 3(m + 1) + 6 = 0
9 − 3m − 3 + 6 = 0
12 − 3m = 0
3m = 12 ⇒ m = 4
Step 2: Find the second root
x2 − (4 + 1) x + 6 = 0 ⇒ x2 − 5x + 6 = 0
x2 − 5x + 6 = (x − 3) (x − 2) = 0
The roots are: x = 3 and x = 2
m = 4, Roots: x = 3 and x = 2
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