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If the equation 2x^2 + 3x - 5 = 0 has roots r1 and r2, what is the value of r1 +

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Question: If the equation 2x^2 + 3x - 5 = 0 has roots r1 and r2, what is the value of r1 + r2?

Options:

  1. -3/2
  2. 3/2
  3. 5/2
  4. -5/2

Correct Answer: -3/2

Solution: 

Using Vieta\'s formulas, r1 + r2 = -b/a = -3/2.

If the equation 2x^2 + 3x - 5 = 0 has roots r1 and r2, what is the value of r1 +

Practice Questions

Q1
If the equation 2x^2 + 3x - 5 = 0 has roots r1 and r2, what is the value of r1 + r2?
  1. -3/2
  2. 3/2
  3. 5/2
  4. -5/2

Questions & Step-by-Step Solutions

If the equation 2x^2 + 3x - 5 = 0 has roots r1 and r2, what is the value of r1 + r2?
  • Step 1: Identify the coefficients in the equation 2x^2 + 3x - 5 = 0. Here, a = 2, b = 3, and c = -5.
  • Step 2: Recall Vieta's formulas, which relate the coefficients of a polynomial to sums and products of its roots.
  • Step 3: According to Vieta's formulas, the sum of the roots (r1 + r2) is given by the formula -b/a.
  • Step 4: Substitute the values of b and a into the formula: r1 + r2 = -3/2.
  • Step 5: Simplify the expression to find the value of r1 + r2.
  • Vieta's Formulas – Vieta's formulas relate the coefficients of a polynomial to sums and products of its roots.
  • Quadratic Equations – Understanding the standard form of a quadratic equation and how to identify coefficients.
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