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x^(2)-10 x+21=0 Let x=h and x=m be solutions to the given equation, with h > m. What is the value of h-m ?

x2−10x+21=0 x^{2}-10 x+21=0 \newlineLet x=h x=h and x=m x=m be solutions to the given equation, with h>m . What is the value of h−m h-m ?

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Q. x2−10x+21=0 x^{2}-10 x+21=0 \newlineLet x=h x=h and x=m x=m be solutions to the given equation, with h>m h>m . What is the value of h−m h-m ?
  1. Identify Quadratic Equation: Identify the quadratic equation to solve.\newlineThe given equation is x2−10x+21=0x^2 - 10x + 21 = 0. We need to find the values of xx that satisfy this equation.
  2. Factor the Equation: Factor the quadratic equation.\newlineWe need to find two numbers that multiply to 2121 and add up to −10-10. The numbers −3-3 and −7-7 satisfy these conditions because (−3)×(−7)=21(-3) \times (-7) = 21 and (−3)+(−7)=−10(-3) + (-7) = -10.\newlineSo, we can write the equation as (x−3)(x−7)=0(x - 3)(x - 7) = 0.
  3. Solve for x: Solve for x using the factored form.\newlineSet each factor equal to zero and solve for x:\newlinex−3=0x - 3 = 0 or x−7=0x - 7 = 0.\newlineThis gives us two solutions: x=3x = 3 or x=7x = 7.
  4. Identify Values of h and m: Identify the values of h and m.\newlineSince h > m, we assign the larger value to h and the smaller value to m. Therefore, h = 77 and m = 33.
  5. Calculate Difference h−m h - m : Calculate the difference h−m h - m .\newlineSubtract the value of m m from h h to find the difference:\newlineh−m=7−3=4 h - m = 7 - 3 = 4 .

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