Question

find the value of 'a' when the expression x³+x²-2ax+a² has a remainder 8 when divided by x-2​

Answer 1

Answer:

the value of a in the given polynomial is 2

Answer 2

Value of a = 2

GIVEN :- $p(x) = {x}^{3} + {x}^{2} - 2ax + {a}^{2}$

Remainder = 8 ; divisor = (x - 2)

To Find :- value of a

SOLUTION:-

• According to remainder theorem , if p(x) is divided by (x -y) then remainder is p(y).
• Similarly if p(x) is divided by (x -2) then remainder is p(2).
• Therefore value of x = 2
• p(x) = 8 given

By substituting the value of x in p(x)

$p(x)= {2}^{3} + {2}^{2} - (2 \times a \times 2) + {a}^{2} \\ 8 = 8 + 4 - 4a + {a}^{2 }$

By rearranging,

${a }^{2} - 4a + 12 = 8$

${a}^{2} - 4a + 12 - 8 = 0 \\ {a}^{2} - 4a + 4 = 0$

By breaking (-4a) into (-2a- 2a)

${a}^{2} - 2a - 2a + 4 = 0 \\ a(a - 2) - 2(a - 2) = 0 \\ (a - 2)(a - 2) = 0$

Therefore,

$a - 2 = 0 \\ a = 2$

Hence value of a = 2

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