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x^(2)+kx-14=0 In the given equation, k is a constant. The equation has solutions at 7 and -2 . What is the value of k ? Choose 1 answer: (A) -9 (B) -5 (c) 5 (D) 9

x2+kx−14=0 x^{2}+k x-14=0 \newlineIn the given equation, k k is a constant. The equation has solutions at 77 and −2-2 . What is the value of k k ?\newlineChoose 11 answer:\newline(A) −9-9\newline(B) −5-5\newline(C) 55\newline(D) 99

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Full solution

Q. x2+kx−14=0 x^{2}+k x-14=0 \newlineIn the given equation, k k is a constant. The equation has solutions at 77 and −2-2 . What is the value of k k ?\newlineChoose 11 answer:\newline(A) −9-9\newline(B) −5-5\newline(C) 55\newline(D) 99
  1. Use Given Solutions: Since the solutions to the quadratic equation are given as 77 and −2-2, we can use the fact that if x=ax = a and x=bx = b are solutions to the equation x2+kx−14=0x^2 + kx - 14 = 0, then the equation can be factored as (x−a)(x−b)=0(x - a)(x - b) = 0.
  2. Factor the Equation: Let's factor the equation using the given solutions: (x−7)(x+2)=0(x - 7)(x + 2) = 0.
  3. Expand Factored Form: Now, we expand the factored form to find the quadratic equation: x2−7x+2x−14=x2−5x−14=0x^2 - 7x + 2x - 14 = x^2 - 5x - 14 = 0.
  4. Compare Coefficients: Comparing the expanded form x2−5x−14=0x^2 - 5x - 14 = 0 with the given equation x2+kx−14=0x^2 + kx - 14 = 0, we can see that the coefficient of xx must be equal to kk. Therefore, k=−5k = -5.

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