In each of the following two polynomials- find the value of a- if x minus- a is nbsp- factor-i- x6 minus- ax5 - x4 minus- ax3 - 3x minus- a - 2-ii x5 minus- a2x3 - 2x - a - 1-

(i) Let be the given polynomial.By factor theorem, (x minus; a) is a factor of the polynomial if nbsp;f(a) = 0Therefore,Thus, the value of a is minus; ...

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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 factor:

(i) x⁶ − ax⁵ + x⁴ − ax³ + 3x − a + 2

(ii x⁵ − a²x³ + 2x + a + 1)

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Solution

(i) Let be the given polynomial.
By factor theorem, (x − a) is a factor of the polynomial if f(a) = 0
Therefore,
Thus, the value of a is − 1.
(ii) Let be the given polynomial.
By factor theorem, (x − a) is a factor of f(x), if f(a) = 0.
Therefore,
Thus, the value of a is − 1/3.

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

(i) x⁶ − ax⁵ + x⁴ − ax³ + 3x − a + 2

(ii x⁵ − a²x³ + 2x + a + 1)

Find the value of a if (x-a) is a factor of the polynomial.

x⁶- ax⁵+ x⁴- ax³+ 3x- a+ 2

Q. Find the value of

a

, if

(x - a)

is a factor of the polynomial,

x^{6} - a x^{5} + x^{4} - a x^{3} + 3 x - a + 2

=0.

The value of $a$ if $(x - a)$ factor of $x^{6} - a x^{5} + x^{4} - a x^{3} + 3 x - a + 2 = 0$ is

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

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

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

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In each of the following two polynomials, find the value of a, if x − a is factor: (i) x6 − ax5 + x4 − ax3 + 3x − a + 2 (ii x5 − a2x3 + 2x + a + 1)

(i) Let be the given polynomial.By factor theorem, (x − a) is a factor of the polynomial if f(a) = 0Therefore,Thus, the value of a is − 1.(ii) Let be the given polynomial.By factor theorem, (x − a) is a factor of f(x), if f(a) = 0.Therefore,Thus, the value of a is − 1/3.

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

(i) x⁶ − ax⁵ + x⁴ − ax³ + 3x − a + 2

(ii x⁵ − a²x³ + 2x + a + 1)

(i) Let be the given polynomial.
By factor theorem, (x − a) is a factor of the polynomial if f(a) = 0
Therefore,
Thus, the value of a is − 1.
(ii) Let be the given polynomial.
By factor theorem, (x − a) is a factor of f(x), if f(a) = 0.
Therefore,
Thus, the value of a is − 1/3.