Find the values of a and b, if x² − 4 is a factor of ax⁴ + 2x³ − 3x² + bx − 4

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Solution

Let and be the given polynomial.

We have,

are the factors of g(x).

By factor theorem, if and both are the factor of f(x)

Then f(2) and f(−2) are equal to zero.

Therefore,

and

Adding these two equations, we get

Putting the value of a in equation (i), we get

Hence, the value of a and b are 1, − 8 respectively.

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Find the values of a and b, if $x^{2}$ - 4 is a factor of $a x^{4} + 2 x^{3} - 3 x^{2}$ + bx - 4

Respected Sir,

Please help me in solving my below mentioned doubt:

Find the values of a and b, if x² - 4 is a factor of ax⁴ + 2x³ - 3x² + bx - 4.

{(a x)}^{4} + 2 x - {3 x}^{2} + b x - 4

x^{2} - 4

2 x^{3} + a x^{2} + b x + 12

Find the value of a for which (x - 4) is a factor of $(2 x^{3} - 3 x^{2} - 18 x + a)$ .

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