285,694 views
27 votes
27 votes
The expressions 2(x² - 4x − 21) - (x − 7) (x +77) and (x − 7) (x + k) are equivalent. - What must be the value of k?​

User Giraffe Lion
by
2.6k points

2 Answers

14 votes
14 votes

Answer:

the value of k must be 2.

Explanation:

To find the value of k, we can set the two expressions equal to each other and solve for k. We have:

2(x² - 4x − 21) - (x − 7) (x +77) = (x − 7) (x + k)

Expanding the left side gives:

2x² - 8x - 42 - x² + 7x + 77 = x² - 7x + kx - 7k

Combining like terms on both sides gives:

x² - 15x + 119 - 7k = 0

This is a quadratic equation in the form ax² + bx + c = 0. To solve for x, we can use the quadratic formula:

x = (-b ± √(b² - 4ac)) / (2a)

Substituting the values for a, b, and c, we get:

x = (15 ± √(225 - 4(1)(119 - 7k))) / 2

Since we are only interested in the value of k, we can disregard the solutions for x. Solving for k, we find that:

k = (-119 + 225 - 4(1)(15)) / (2(-7))

Simplifying this expression gives:

k = (-119 + 225 + 60) / (-14)

k = (-34) / (-14)

k = 34/14

k = 2

Therefore, the value of k must be 2.

User Zhuo
by
2.6k points
14 votes
14 votes

Answer:

-71

Explanation:

The constant term of
2(x^2-4x-21)-(x-7)(x+77) is
2(-21)-(-7)(77)=497.

The constant term of
(x-7)(x+k) is
-7k.

So,
497=-7k \implies k=-71.

User Jyo The Whiff
by
2.7k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.