In this page equation from roots solution5 we are going to see solution for the worksheet framing quadratic equation from roots.

Find quadratic polynomials each with the given numbers as sum and product of its zeroes respectively.

(i) Let α and β are the roots of a quadratic equation

Sum of the zeroes = 3

α + β = 3

Product of zeroes = 1

α β = 1

One of the such polynomial is p(x) = x² - (α + β) x + α β

= x² - 3 x + 1

(ii) Let α and β are the roots of a quadratic equation

Sum of the zeroes = 2

α + β = 2

Product of zeroes = 4

α β = 4

One of the such polynomial is p(x) = x² - (α + β) x + α β

= x² - 2 x + 4

(iii) Let α and β are the roots of a quadratic equation

Sum of the zeroes = 0

α + β = 0

Product of zeroes = 4

α β = 4

One of the such polynomial is p(x) = x² - (α + β) x + α β

= x² - 0 x + 4

= x² + 4

(iv) Let α and β are the roots of a quadratic equation

Sum of the zeroes = √2

α + β = √2

Product of zeroes = 1/5

α β = 1/5

One of the such polynomial is p(x) = x² - (α + β) x + α β

= x² - √2 x + (1/5)

= 5x² - √2 x + 1

(v) Let α and β are the roots of a quadratic equation

Sum of the zeroes = 1/3

α + β = 1/3

Product of zeroes = 1

α β = 1

One of the such polynomial is p(x) = x² - (α + β) x + α β

= x² – (1/3) x + 1

= 3x² - x + 3

(vi) Let α and β are the roots of a quadratic equation

Sum of the zeroes = 1/2

α + β = 1/2

Product of zeroes = -4

α β = -4

One of the such polynomial is p(x) = x² - (α + β) x + α β

= x² – (1/2) x - 4

= 2 x² - x - 8

(vii) Let α and β are the roots of a quadratic equation

Sum of the zeroes = 1/3

α + β = 1/3

Product of zeroes = -1/3

α β = -1/3

One of the such polynomial is p(x) = x² - (α + β) x + α β

= x² – (1/3) x + (-1/3)

= 3 x² - x - 1

(viii) Let α and β are the roots of a quadratic equation

Sum of the zeroes = √3

α + β = √3

Product of zeroes = 2

α β = 2

One of the such polynomial is p(x) = x² - (α + β) x + α β

= x² – √3 x + 2

equation from roots solution5 equation from roots solution5 equation from roots solution5

- Synthetic division
- Rational Expressions
- Rational Zeros Theorem
- LCM -Least Common Multiple
- GCF-Greatest Common Factor
- Simplifying Rational Expressions
- Factorize of Polynomials
- Factoring worksheet
- Framing Quadratic Equation Worksheet
- Remainder Theorem
- Relationship Between Coefficients and roots
- Roots of Cubic equation
- Roots of Polynomial of Degree4
- Roots of Polynomial of Degree5
- System Of Linear Equations

quadratic equation from roots