In each of the following two polynomials- find the value of a- if x-a is factor-i x6-a x5-x4-a x3-3 x-a-2ii -x5-a2 x3-2 x-a-1

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

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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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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

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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.

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

Determine which of the following polynomials has (x + 1) a factor:

(i) x³ + x² + x + 1 (ii) x⁴ + x³ + x² + x + 1

(iii) x⁴ + 3x³ + 3x² + x + 1 (iv)

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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) = 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.

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.