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⇒ The roots of the quadratic equation ax2 bx c = 0, a ≠ 0 can be found by using the following formula, if its discriminant (D = b2 - 4ac) is greater than or equal to zero. Can anyone explain this.?
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⇒ The roots of the quadratic equation ax2 bx c = 0, a ≠ 0 can be f...
Explanation of the Quadratic Formula:
The roots of a quadratic equation of the form ax^2 + bx + c = 0 can be found using the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / 2a
Discriminant and its significance:
The discriminant of a quadratic equation is given by D = b^2 - 4ac. It determines the nature of the roots of the equation.
- If the discriminant is greater than zero (D > 0), the equation has two distinct real roots.
- If the discriminant is equal to zero (D = 0), the equation has one real root (a repeated root).
- If the discriminant is less than zero (D < 0),="" the="" equation="" has="" two="" complex="" />
Using the Discriminant to Find Roots:
1. Calculate the discriminant D = b^2 - 4ac.
2. If D is greater than or equal to zero, proceed to find the roots using the quadratic formula.
3. Substitute the values of a, b, and c into the formula x = (-b ± √D) / 2a.
4. Simplify the expression to find the roots of the quadratic equation.
Example:
Consider the quadratic equation 2x^2 + 5x - 3 = 0.
Here, a = 2, b = 5, and c = -3.
Calculate the discriminant: D = 5^2 - 4(2)(-3) = 25 + 24 = 49 (D > 0).
Using the quadratic formula: x = (-5 ± √49) / 4.
Therefore, the roots are x = (-5 + 7) / 4 = 2/4 = 0.5 and x = (-5 - 7) / 4 = -12/4 = -3.
By following these steps and understanding the significance of the discriminant, you can easily find the roots of a quadratic equation.
The roots of a quadratic equation of the form ax^2 + bx + c = 0 can be found using the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / 2a
Discriminant and its significance:
The discriminant of a quadratic equation is given by D = b^2 - 4ac. It determines the nature of the roots of the equation.
- If the discriminant is greater than zero (D > 0), the equation has two distinct real roots.
- If the discriminant is equal to zero (D = 0), the equation has one real root (a repeated root).
- If the discriminant is less than zero (D < 0),="" the="" equation="" has="" two="" complex="" />
Using the Discriminant to Find Roots:
1. Calculate the discriminant D = b^2 - 4ac.
2. If D is greater than or equal to zero, proceed to find the roots using the quadratic formula.
3. Substitute the values of a, b, and c into the formula x = (-b ± √D) / 2a.
4. Simplify the expression to find the roots of the quadratic equation.
Example:
Consider the quadratic equation 2x^2 + 5x - 3 = 0.
Here, a = 2, b = 5, and c = -3.
Calculate the discriminant: D = 5^2 - 4(2)(-3) = 25 + 24 = 49 (D > 0).
Using the quadratic formula: x = (-5 ± √49) / 4.
Therefore, the roots are x = (-5 + 7) / 4 = 2/4 = 0.5 and x = (-5 - 7) / 4 = -12/4 = -3.
By following these steps and understanding the significance of the discriminant, you can easily find the roots of a quadratic equation.
Community Answer
⇒ The roots of the quadratic equation ax2 bx c = 0, a ≠ 0 can be f...
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⇒ The roots of the quadratic equation ax2 bx c = 0, a ≠ 0 can be found by using the following formula, if its discriminant (D = b2 - 4ac) is greater than or equal to zero. Can anyone explain this.? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about ⇒ The roots of the quadratic equation ax2 bx c = 0, a ≠ 0 can be found by using the following formula, if its discriminant (D = b2 - 4ac) is greater than or equal to zero. Can anyone explain this.? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for ⇒ The roots of the quadratic equation ax2 bx c = 0, a ≠ 0 can be found by using the following formula, if its discriminant (D = b2 - 4ac) is greater than or equal to zero. Can anyone explain this.?.
⇒ The roots of the quadratic equation ax2 bx c = 0, a ≠ 0 can be found by using the following formula, if its discriminant (D = b2 - 4ac) is greater than or equal to zero. Can anyone explain this.? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about ⇒ The roots of the quadratic equation ax2 bx c = 0, a ≠ 0 can be found by using the following formula, if its discriminant (D = b2 - 4ac) is greater than or equal to zero. Can anyone explain this.? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for ⇒ The roots of the quadratic equation ax2 bx c = 0, a ≠ 0 can be found by using the following formula, if its discriminant (D = b2 - 4ac) is greater than or equal to zero. Can anyone explain this.?.
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