A general form of a quadratic equation ax^{2} + 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
x^{2} – (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
x^{2} + 5x + 6 = 0
Solution :
x^{2} + 5x + 6 = 0
A general form of a quadratic equation ax^{2} + 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
x^{2} - 4x - 10 = 0
Solution :
x^{2} - 4x - 10 = 0
A general form of a quadratic equation ax^{2} + 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
2x^{2} + 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
3x^{2} + 5x - 9 = 0
Solution :
3x^{2} + 5x - 9 = 0
A general form of a quadratic equation ax^{2} + 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
5x^{2} - 7x - 10 = 0
Solution :
5x^{2} - 7x - 10 = 0
A general form of a quadratic equation ax^{2} + 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 |
x^{2} – (α + β)x + αβ = 0
x^{2} – (-3)x + (-70) = 0
x^{2} + 3x - 70 = 0
So, the equation is x^{2} + 3x - 70 = 0.
Feb 25, 24 07:44 AM
Feb 24, 24 11:07 PM
Feb 24, 24 08:49 PM