Question

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

Answer 1

Answer:

• c = 3.09375

Step-by-step explanation:

Standard for of quadratic equation:

• ax² + bx + c = 0

We have

• 2x² - 5x + c = 0

Sum of the roots

• x₁ + x₂ = - b/a = -(-5)/2 = 2.5

Product of the roots

• x₁x₂ = c/a = c / 2

We have:

• x₁ - x₂ = 0.25

The square of the above is:

• (x₁ - x₂)² = (x₁ + x₂)² - 4x₁x₂

Substitute known values and solve for c:

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