SUM AND PRODUCT OF THE ROOTS OF A QUADRATIC EQUATION

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

Question 1 :

x² + 3x - 28 = 0

Solution :

Comparing x² + 3x - 28 = 0 and ax² + bx + c = 0, we get

a = 1, b = 3 and c = -28

Sum of the roots = -b/a

= -3/1

= -3

Product of the roots = c/a

= -28/1

= -28

Question 2 :

x² + 3x = 0

Solution :

Comparing x² + 3x = 0 and ax² + bx + c = 0, we get

a = 1, b = 3 and c = 0

Sum of the roots = -b/a

= -3/1

= -3

Product of the roots (aᵦ) = c/a

= 0/1

= 0

Question 3 :

3 + (1/a) = 10/a²

Solution :

10/a² - (1/a) - 3 = 0

(10 - a - 3a²)/a² = 0

-3a² - a + 10 = 0

In the above quadratic equation, 

coefficient of squared term a = -3,

coefficient of a term = -1

constant term = 10

Sum of the roots = -b/a

= -(-1)/(-3)

= -1/3

Product of the roots = c/a

= 10/(-3)

= -10/3

Question 4 :

3y² - y - 4 = 0

Solution :

Comparing 3y² - y - 4 = 0 and ax² + bx + c = 0,

a = 3, b = -1 and c = -4

Sum of the roots = -b/a

= -(-1)/3

= 1/3

Product of the roots = c/a

= -4/3  

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