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If a(alpha),:b( beta)are zeros of quadratic polynomial 2x^2 - 5x - 6 then form a quadratic polynomial whose zeros are a+b and ab,[ a =alpha b =beta]?
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Finding the Zeros of the Quadratic Polynomial
To find the zeros (roots) of the polynomial 2x^2 - 5x - 6, we can use the quadratic formula:
- The formula is: x = [-b ± √(b² - 4ac)] / (2a)
- Here, a = 2, b = -5, and c = -6.
Calculating the Discriminant
- Discriminant (D) = b² - 4ac
- D = (-5)² - 4(2)(-6) = 25 + 48 = 73
Finding the Roots
- Now, substituting into the quadratic formula:
- x = [5 ± √73] / 4
- Therefore, the roots are:
- a = [5 + √73] / 4
- b = [5 - √73] / 4
Forming the New Polynomial
We need to find a new polynomial whose zeros are a + b and ab.
Calculating a + b and ab
- Using Vieta’s formulas:
- a + b = -(-5)/2 = 5/2
- ab = -6/2 = -3
Creating the New Polynomial
The new quadratic polynomial with zeros a + b and ab can be formed using the standard form:
- The polynomial can be expressed as:
- x² - (sum of roots)x + (product of roots)
Substituting the values:
- New polynomial = x² - (5/2)x - 3
Final Result
Thus, the required quadratic polynomial is:
- 2x² - 5x - 6
This polynomial has the roots a + b and ab, derived from the original polynomial's zeros.
To find the zeros (roots) of the polynomial 2x^2 - 5x - 6, we can use the quadratic formula:
- The formula is: x = [-b ± √(b² - 4ac)] / (2a)
- Here, a = 2, b = -5, and c = -6.
Calculating the Discriminant
- Discriminant (D) = b² - 4ac
- D = (-5)² - 4(2)(-6) = 25 + 48 = 73
Finding the Roots
- Now, substituting into the quadratic formula:
- x = [5 ± √73] / 4
- Therefore, the roots are:
- a = [5 + √73] / 4
- b = [5 - √73] / 4
Forming the New Polynomial
We need to find a new polynomial whose zeros are a + b and ab.
Calculating a + b and ab
- Using Vieta’s formulas:
- a + b = -(-5)/2 = 5/2
- ab = -6/2 = -3
Creating the New Polynomial
The new quadratic polynomial with zeros a + b and ab can be formed using the standard form:
- The polynomial can be expressed as:
- x² - (sum of roots)x + (product of roots)
Substituting the values:
- New polynomial = x² - (5/2)x - 3
Final Result
Thus, the required quadratic polynomial is:
- 2x² - 5x - 6
This polynomial has the roots a + b and ab, derived from the original polynomial's zeros.
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If a(alpha),:b( beta)are zeros of quadratic polynomial 2x^2 - 5x - 6 then form a quadratic polynomial whose zeros are a+b and ab,[ a =alpha b =beta]? for Class 10 2025 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about If a(alpha),:b( beta)are zeros of quadratic polynomial 2x^2 - 5x - 6 then form a quadratic polynomial whose zeros are a+b and ab,[ a =alpha b =beta]? covers all topics & solutions for Class 10 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If a(alpha),:b( beta)are zeros of quadratic polynomial 2x^2 - 5x - 6 then form a quadratic polynomial whose zeros are a+b and ab,[ a =alpha b =beta]?.
If a(alpha),:b( beta)are zeros of quadratic polynomial 2x^2 - 5x - 6 then form a quadratic polynomial whose zeros are a+b and ab,[ a =alpha b =beta]? for Class 10 2025 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about If a(alpha),:b( beta)are zeros of quadratic polynomial 2x^2 - 5x - 6 then form a quadratic polynomial whose zeros are a+b and ab,[ a =alpha b =beta]? covers all topics & solutions for Class 10 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If a(alpha),:b( beta)are zeros of quadratic polynomial 2x^2 - 5x - 6 then form a quadratic polynomial whose zeros are a+b and ab,[ a =alpha b =beta]?.
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