HOW TO FIND THE SUM AND PRODUCT OF ROOTS FROM GIVEN QUADRATIC EQUATION

How to Find the Sum and Product of Roots from Given Quadratic Equation ?

Let a and ᵦ be the roots of the given quadratic equation, by solving the given quadratic equation, we get two roots. In which one is a and the other one is ᵦ.

Sum of roots (a + ᵦ) = -b/a (or)

= - coefficient of x/coefficient of x^{2}

Sum of roots (a ᵦ) = c/a (or)

= constant term/coefficient of x^{2}

How to Find the Sum and Product of Roots from Given Quadratic Equation - Questions

Question 1 :

Find the sum and product of the roots for each of the following quadratic equations

(i) x^{2} + 3x −28 = 0

Solution :

By comparing the given equation x^{2} + 3x −28 = 0, with ax^{2} + bx + c = 0, we get a = 1, b = 3 and c = -28

Sum of zeroes (a + ᵦ) = -3/1 = -3

Product of zeroes (a ᵦ) = -28/1 = -28

Hence the sum and product of zeroes of given quadratic equation are -3 and -28 respectively.

(ii) x^{2} + 3x = 0

Solution :

By comparing the given equation x^{2} + 3x = 0, with ax^{2} + bx + c = 0, we get a = 1, b = 3 and c = 0

Sum of zeroes (a + ᵦ) = -3/1 = -3

Product of zeroes (a ᵦ) = 0/1 = 0

Hence the sum and product of zeroes of given quadratic equation are -3 and 0 respectively.

(iii) 3 + (1/a) = 10/a^{2}

Solution :

10/a^{2 }- (1/a) - 3 = 0

(10 - a - 3a^{2})/a^{2} = 0

- 3a^{2 }- a + 10 = 0

coefficient of squared term a = -3, coefficient of a term = -1 and constant term = 10.

Sum of zeroes (a + ᵦ) = -(-1)/(-3) = -1/3

Product of zeroes (a ᵦ) = 10/(-3) = -10/3

Hence the sum and product of zeroes of given quadratic equation are -1/3 and -10/3 respectively.

(iv) 3y^{2} - y - 4 = 0

Solution :

By comparing the given equation 3y^{2} - y - 4 = 0, with ax^{2} + bx + c = 0, we get a = 3, b = -1 and c = -4

Sum of zeroes (a + ᵦ) = -(-1)/3 = 1/3

Product of zeroes (a ᵦ) = -4/3

Hence the sum and product of zeroes of given quadratic equation are 1/3 and -4/3 respectively.

After having gone through the stuff given above, we hope that the students would have understood, "How to Find the Sum and Product of Roots from Given Quadratic Equation".

Apart from the stuff given in this section "How to Find the Sum and Product of Roots from Given Quadratic Equation", if you need any other stuff in math, please use our google custom search here.