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प्रश्न
In the following two polynomials. Find the value of ‘a’ if x + a is a factor of each of the two:
x3 + ax2 − 2x + a + 4
Find the value of a if x + a is a factor of x3 + ax2 − 2x + a + 4.
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उत्तर
Let p(x) = x3 + ax2 − 2x + a + 4 ...(i)
Since, (x + a) is a factor of p(x),
So p(−a) = 0
Put x = −a in equation (i), we get
p(−a) = (−a)3 + a(−a)2 − 2(−a) + a + 4
= −a3 + a(a2) + 2a + a + 4
= −a3 + a3 + 3a + 4
= 3a + 4
But p(−a) = 0
⇒ 3a + 4 = 0
⇒ 3a = −4
⇒ a = `−4/3`
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