Question
If x4 + 2x3 + ax2 + bx + 9 is a perfect square where a and b are positive real numbers, then the value of a and b is?
Answer: Option B
$$\eqalign{
& {x^4} + 2{x^3} + a{x^2} + bx + 9 \cr
& {\text{Put }}x = 1 \cr
& = 1 + 2 \times 1 + a + b + 9 \cr
& = 1 + 2 + a + b + 9 \cr
& = 13 + a + b \cr} $$
To make a perfect square numbers value of a + b must be either 3 or 13
Now, option (B) a = 6, b = 7
$$\eqalign{
& \therefore a + b = 13 \cr
& {\text{make perfect square}} \cr
& \left( {25 = {5^2}} \right) \cr} $$
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$$\eqalign{
& {x^4} + 2{x^3} + a{x^2} + bx + 9 \cr
& {\text{Put }}x = 1 \cr
& = 1 + 2 \times 1 + a + b + 9 \cr
& = 1 + 2 + a + b + 9 \cr
& = 13 + a + b \cr} $$
To make a perfect square numbers value of a + b must be either 3 or 13
Now, option (B) a = 6, b = 7
$$\eqalign{
& \therefore a + b = 13 \cr
& {\text{make perfect square}} \cr
& \left( {25 = {5^2}} \right) \cr} $$
Was this answer helpful ?
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