Find Number Of Real Solutions Using Discriminant Worksheet

Algebra 2
Quadratic Equations

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How Will This Worksheet on “Find Number of Real Solutions Using Discriminant” Benefit Your Student's Learning?

  • It deepens our understanding of the nature of solutions for quadratic equations.
  • It enhances our ability to analyze and evaluate mathematical problems, promoting logical and critical thinking skills.
  • It improves problem-solving abilities by helping us determine the number and type of solutions available.

How to Find Number of Real Solutions Using Discriminant?

  • Identify the values of \(a\), \(b\), and \(c\) from the given quadratic equation.
  • Plug the values of \(a\), \(b\), and \(c\) into the discriminant formula.
  • Compute the value of \(D\).
  • Examine the discriminant to determine the nature of the roots.

Solved Example

Q. Determine the number of real solutions for the quadratic equation 2x23x+1=02x^2 - 3x + 1 = 0 using the discriminant.
Solution:
  1. Identify values: Identify the values of aa, bb, and cc.\newlineCompare ax2+bx+c=0ax^2 + bx + c = 0 and 2x23x+1=02x^2 - 3x + 1 = 0.\newlinea=2a = 2\newlineb=3b = -3\newlinec=1c = 1
  2. Compare equations: Substitute a=2a = 2, b=3b = -3, and c=1c = 1 into the discriminant formula D=b24acD = b^2 - 4ac.\newlineD=(3)2421D = (-3)^2 - 4 \cdot 2 \cdot 1
  3. Substitute into formula: Simplify the discriminant.\newlineD=98D = 9 - 8
  4. Simplify discriminant: Calculate the final value of the discriminant.\newlineD=1D = 1
  5. Calculate final value: Determine the number of real solutions based on the discriminant.\newlineSince D>0D > 0, there are 22 real solutions.
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About Worksheet

Algebra 2
Quadratic Equations

The discriminant is essential in quadratic equations for determining the nature of the roots. For the quadratic equation \(ax^2 + bx + c = 0\), the discriminant is calculated as \(b^2 - 4ac\).

The value of the discriminant indicates:

If \(D > 0\): Two distinct real roots.

If \(D = 0\): One real root (repeated).

If \(D < 0\): No real roots.

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