FIND THE SUM AND PRODUCT OF ROOTS OF A QUADRATIC EQUATION

A general form of a quadratic equation ax2 + bx + c = 0

To find the sum and product of the roots of the quadratic equation,

Sum of the roots = -b/a

Products of the roots = c/a

If α, β, are the roots of the quadratic equation, then the form of the quadratic equation as

x2 – (α + β)x + αβ = 0

Where,

α + β = sum of roots

αβ = product of roots

Problem 1 :

Find the sum and product of roots of the quadratic equation

x2 + 5x + 6 = 0

Solution :

x2 + 5x + 6 = 0

A general form of a quadratic equation ax2 + bx + c = 0

a = 1, b = 5, c = 6

Sum of the roots = -b/a = -5/1 = -5

Products of the roots = c/a = 6/1 = 6

So, the sum and products of the roots are -5 and 6 respectively.

Problem 2 :

Find the sum and product of roots of the quadratic equation

x2 - 4x - 10 = 0

Solution :

x2 - 4x - 10 = 0

A general form of a quadratic equation ax2 + bx + c = 0

a = 1, b = -4, c = -10

Sum of the roots = -b/a = -(-4)/1 = 4

Products of the roots = c/a = -10/1 = -10

So, the sum and products of the roots are 4 and 10 respectively.

Problem 3 :

Find the sum and product of roots of the quadratic equation

2x2 + 6x + 8 = 0

Solution :

2x2 + 6x + 8 = 0

A general form of a quadratic equation ax2 + bx + c = 0

a = 2, b = 6, c = 8

Sum of the roots = -b/a = -6/2 = -3

Products of the roots = c/a = 8/2 = 4

So, the sum and products of the roots are -3 and 4 respectively.

Problem 4 :

Find the sum and product of roots of the quadratic equation

3x2 + 5x - 9 = 0

Solution :

3x2 + 5x - 9 = 0

A general form of a quadratic equation ax2 + bx + c = 0

a = 3, b = 5, c = -9 

Sum of the roots = -b/a = -5/3 

Products of the roots = c/a = -9/3 = -3

So, the sum and products of the roots are -5/3 and -3 respectively.

Problem 5 :

Find the sum and product of roots of the quadratic equation

5x2 - 7x - 10 = 0

Solution :

5x2 - 7x - 10 = 0

A general form of a quadratic equation ax2 + bx + c = 0

a = 5, b = -7, c = -10

Sum of the roots = -b/a = -(-7)/5 = 7/5 

Products of the roots = c/a = -10/5 = -2

So, the sum and products of the roots are 7/5 and -2 respectively.

Problem 6 :

Form the equation whose roots are 7and -10.

Solution :

Given, roots are 7and -10

Sum of the roots = α + β 

Product of roots = αβ

 α = 7, β = -10

α + β = 7 + (-10)

= 7 – 10

α + β = -3

αβ = 7 × (-10)

αβ = -70

x2 – (α + β)x + αβ = 0

x2 – (-3)x + (-70) = 0

x2 + 3x - 70 = 0

So, the equation is x2 + 3x - 70 = 0.

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