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प्रश्न
If (x - 2) is a factor of x3 − mx2 + 10x − 20 then find the value of m.
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उत्तर
Let p(x) = x3 − mx2 + 10x − 20
(x − 2) is a factor of p(x) = x3 − mx2 + 10x − 20
By factor theorem,
remainder = 0
∴ p(2) = 0
⇒ (2)3 − m × (2)2 + 10 × (2) − 20 = 0
⇒ 8 − 4m + 20 − 20 = 0
⇒ 8 − 4m = 0
⇒ 4m = 8
⇒ m = 2
Thus, the value of m is 2.
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