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kakasveta [241]
3 years ago
15

The diffrence between the roots of the equation 2x^2-5x+c=0 is 0.25 find c

Mathematics
1 answer:
kumpel [21]3 years ago
6 0

Answer:

  • c = 3.09375

Step-by-step explanation:

<u>Standard for of quadratic equation:</u>

  • ax² + bx + c = 0

<u>We have </u>

  • 2x² - 5x + c = 0

<u>Sum of the roots </u>

  • x₁ + x₂ = - b/a = -(-5)/2 = 2.5

<u>Product of the roots </u>

  • x₁x₂ = c/a = c / 2

<u>We have:</u>

  • x₁ - x₂ = 0.25

<u>The square of the above is:</u>

  • (x₁ - x₂)² = (x₁ + x₂)² - 4x₁x₂

<u>Substitute known values and solve for c:</u>

  • 0.25² = (2.5)² - 4(c/2)
  • 2c = 6.25 - 0.0625
  • 2c = 6.1875
  • c = 3.09375
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