Question

What should be the value of a, in the polynomials x2 11x + a and x2 14x + 2a, so that these two polynomials have common factors. A) 24 b)1 c)-1 d)1/2

Answer 1

Answer:

c)-1

Step-by-step explanation:

The above question is simplified and the answer is option c)-1

Answer 2

The value of 'a' is 24.

Option A is correct.

Given:

• Two quadratic polynomials.
• ${x}^{2} - 11x + a$ and ${x}^{2} - 14x + 2a$

To find:

• Find the value of 'a' if both the polynomials have one common factor.

• A) 24
• B) 1
• C) -1
• D) 1/2.

Solution:

Concept to be used:

• Apply factor theorem.
• The factor of the polynomial satisfies the polynomial.

Step 1:

Let the common factor of polynomials be 'n'.

According to the factor theorem concept.

${n}^{2} - 11n + a = 0 \\ {n}^{2} - 14n + 2a = 0$

Step 2:

Apply the crammer's rule.

$\frac{ {n}^{2} }{ - 22 a+ 14a} = \frac{ - n}{2a - a} = \frac{1}{ - 14 + 11}$

$\frac{ {n}^{2} }{ - 8a} = \frac{ - n}{a} = \frac{1}{ - 3}$

from the last two terms

$\frac{ {n}^{2} }{ - 8a} = \frac{ - n}{a}$

Cancel the common terms from both terms

$\frac{ {n}}{ 8} = \frac{ 1}{1}$

$\bf n = 8$

Step 3:

Calculate the value of a.

Put the value of n in any of the equations to calculate the value of a.

${(8)}^{2} - 11 \times 8 + a = 0$

$64 - 88 + a = 0$

$a - 24= 0$

$\bf a = 24$

Thus,

The value of 'a' is 24.

Option A is correct.

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