Question The expressions 2(x² – 4x − 21) – (x − 7) (x +77) and (x − 7) (x + k) are equivalent. – What must be the value of k?

Answer: -71 Step-by-step explanation: The constant term of is . The constant term of is . So, . Reply

Answer: the value of k must be 2. Step-by-step 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. Reply

Answer:Step-by-step explanation:Answer:Step-by-step explanation: