RELATIONSHIP BETWEEN ZEROES AND COEFFICIENTS OF A QUADRATIC POLYNOMIAL





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 problems on relationship between zeros and coefficients of a quadratic polynomial:

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






Relationship Between Coefficients androots to Algebra