In each of the following two polynomials- find the value of a- if x - a is a factor-i- x3 - ax2 minus- 2x -a - 4-ii- x4 minus- a2x2 - 3x minus-a

(i) Let be the given polynomial.By the factor theorem, (+ a) is the factor of f(x), if f( minus; a) = 0, i.e.,Thus, the value of a is minus; 4/3.(ii) Let ...

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Standard IX

Mathematics

Polynomials

In each of th...

Question

In each of the following two polynomials, find the value of a, if x + a is a factor.

(i) x³ + ax² − 2x +a + 4

(ii) x⁴ − a²x² + 3x −a

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Solution

(i) Let be the given polynomial.
By the factor theorem, (+ a) is the factor of f(x), if f(− a) = 0, i.e.,
Thus, the value of a is − 4/3.
(ii) Let be the polynomial. By factor theorem, (x + a) is a factor of the f(x), if f(− a) = 0, i.e.,
Thus, the value of a is 0.

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In each of the following, two polynomials, find the value of a, if x + a is a factor.

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

Q. In each of the following two polynomials, find the value of a, if x − a is factor:

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I.

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Q. If the polynomials

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and

x^{3} + x^{2} - 4 x + a

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In each of the following two polynomials, find the value of a, if x + a is a factor. (i) x3 + ax2 − 2x +a + 4 (ii) x4 − a2x2 + 3x −a

(i) Let be the given polynomial.By the factor theorem, (+ a) is the factor of f(x), if f(− a) = 0, i.e.,Thus, the value of a is − 4/3.(ii) Let be the polynomial. By factor theorem, (x + a) is a factor of the f(x), if f(− a) = 0, i.e.,Thus, the value of a is 0.

In each of the following two polynomials, find the value of a, if x + a is a factor.

(i) x³ + ax² − 2x +a + 4

(ii) x⁴ − a²x² + 3x −a

(i) Let be the given polynomial.
By the factor theorem, (+ a) is the factor of f(x), if f(− a) = 0, i.e.,
Thus, the value of a is − 4/3.
(ii) Let be the polynomial. By factor theorem, (x + a) is a factor of the f(x), if f(− a) = 0, i.e.,
Thus, the value of a is 0.