In this page relationship between zeros and coefficients of a quadratic polynomial we are going see how to find sum and product roots of any quadratic equation.

Procedure to find relationship:

Consider
the equation ax² + bx + c = 0. where a,b and c ∈ R. We can solve this
quadratic equation by using quadratic formula. Then we get α and β as
two roots of the equation. Now we are going to see the concept how to
find sum of roots **α + β** and product of roots **α β**.

Formula:

Sum of roots α + β = -b/a

Product of roots α β = c/a

Values of a,b and c can get from the quadratic equation.

**Example 1:**

Determine the sum and product of roots of the equation x² - 8 x + 24 = 0

**Solution :**

x² - 8 x + 24 = 0

ax² + bx + c = 0

a = 1, b = -8 and c = 24

Sum of roots α + β = -b/a

α + β = -(-8)/1

α + β = 8

Product of roots α β = c/a

α β = 24/1

α β = 24

**Example 2:**

If one of the root of the quadratic equation 2x² - 11 x - 6 = 0 is 6 find the other root.

**Solution :**

2x² - 11 x - 6 = 0

ax² + bx + c = 0

a = 2, b = -11 and c = -6

One of the root (α) = 6

Sum of roots α + β = -b/a

α + β = -(-11)/2

α + β = 11/2

Product of roots α β = -6/2

α β = -3

6 β = -3

β = -3/6

β = -1/2

Therefore another root = -1/2

These are the examples in the topic relationship between zeros and coefficients of a quadratic polynomial

**Example 3:**

Determine the sum and product of roots of the equation 2 x² - 5 x + 4 = 0

**Solution :**

2 x² - 5 x + 4 = 0

ax² + bx + c = 0

a = 2, b = -5 and c = 4

Sum of roots α + β = -b/a

α + β = -(-5)/2

α + β = 5/2

Product of roots α β = c/a

α β = 4/2

α β = 2

- Practice questions on relationship between roots
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- Rational Expressions
- Rational Zeros Theorem
- LCM -Least Common Multiple
- GCF-Greatest Common Factor
- Simplifying Rational Expressions
- Factorize of Polynomials
- Framing Quadratic Equation From Roots
- 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