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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 please explain this.?
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⇒ The roots of the quadratic equation ax2 bx c = 0, a ≠ 0 can be f...
Quadratic Equations and its Roots:
A quadratic equation is a second-degree polynomial equation in the form of ax^2 + bx + c = 0, where a, b, and c are constants and 'x' is the variable. The roots of a quadratic equation are the values of 'x' that satisfy the equation and make it equal to zero.
Discriminant:
The discriminant of a quadratic equation is a mathematical term that helps us determine the nature and number of roots of the equation. It is calculated using the formula D = b^2 - 4ac, where 'D' represents the discriminant and 'a', 'b', and 'c' are the coefficients of the quadratic equation.
Conditions for Finding Roots:
To find the roots of a quadratic equation using the formula, we need to consider the value of the discriminant. The discriminant can be categorized into three cases:
1. D > 0:
If the discriminant is greater than zero (D > 0), it implies that the quadratic equation has two distinct real roots. In this case, the formula to find the roots is given by:
x = (-b ± √D) / (2a)
The two roots are obtained by substituting the positive and negative values of the square root of the discriminant.
2. D = 0:
If the discriminant is equal to zero (D = 0), it means that the quadratic equation has two identical real roots. In this case, the formula to find the roots simplifies to:
x = -b / (2a)
The single root is obtained by substituting zero in the square root term of the formula.
3. D < />
If the discriminant is less than zero (D < 0),="" it="" indicates="" that="" the="" quadratic="" equation="" has="" no="" real="" roots.="" instead,="" it="" has="" two="" complex="" conjugate="" roots.="" complex="" numbers="" involve="" the="" imaginary="" unit="" 'i',="" where="" i^2="-1." therefore,="" the="" roots="" can="" be="" expressed="" />
x = (-b ± i√(-D)) / (2a)
The two complex roots are obtained by substituting the positive and negative values of the square root of the absolute value of the discriminant multiplied by 'i'.
Conclusion:
By considering the discriminant of a quadratic equation, we can determine the nature and number of roots it possesses. If the discriminant is greater than or equal to zero, we can use the quadratic formula to find the roots. The discriminant acts as a key factor in solving quadratic equations and helps us understand their behavior in terms of roots.
A quadratic equation is a second-degree polynomial equation in the form of ax^2 + bx + c = 0, where a, b, and c are constants and 'x' is the variable. The roots of a quadratic equation are the values of 'x' that satisfy the equation and make it equal to zero.
Discriminant:
The discriminant of a quadratic equation is a mathematical term that helps us determine the nature and number of roots of the equation. It is calculated using the formula D = b^2 - 4ac, where 'D' represents the discriminant and 'a', 'b', and 'c' are the coefficients of the quadratic equation.
Conditions for Finding Roots:
To find the roots of a quadratic equation using the formula, we need to consider the value of the discriminant. The discriminant can be categorized into three cases:
1. D > 0:
If the discriminant is greater than zero (D > 0), it implies that the quadratic equation has two distinct real roots. In this case, the formula to find the roots is given by:
x = (-b ± √D) / (2a)
The two roots are obtained by substituting the positive and negative values of the square root of the discriminant.
2. D = 0:
If the discriminant is equal to zero (D = 0), it means that the quadratic equation has two identical real roots. In this case, the formula to find the roots simplifies to:
x = -b / (2a)
The single root is obtained by substituting zero in the square root term of the formula.
3. D < />
If the discriminant is less than zero (D < 0),="" it="" indicates="" that="" the="" quadratic="" equation="" has="" no="" real="" roots.="" instead,="" it="" has="" two="" complex="" conjugate="" roots.="" complex="" numbers="" involve="" the="" imaginary="" unit="" 'i',="" where="" i^2="-1." therefore,="" the="" roots="" can="" be="" expressed="" />
x = (-b ± i√(-D)) / (2a)
The two complex roots are obtained by substituting the positive and negative values of the square root of the absolute value of the discriminant multiplied by 'i'.
Conclusion:
By considering the discriminant of a quadratic equation, we can determine the nature and number of roots it possesses. If the discriminant is greater than or equal to zero, we can use the quadratic formula to find the roots. The discriminant acts as a key factor in solving quadratic equations and helps us understand their behavior in terms of roots.
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⇒ The roots of the quadratic equation ax2 bx c = 0, a ≠ 0 can be f...
Check your question signs b/w the quadratic equation is missing
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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 please explain this.?
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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 please 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 please 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 please 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 please 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 please 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 please explain this.?.
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