Maths
General
Easy
Question
What is the sum of the solutions to the given equation?


 14
 16
The correct answer is: 16
The given equation is a quadratic equation (i.e. Highest power of a variable is 2). We will solve the given quadratic equation and find the sum of the solutions so obtained.
Stepbystep solution:
x^{2}  14x + 40 = 2x + 1
x^{2 } 14x  2x + 40  1 = 0
x^{2}  16x +39 = 0  (equation i)
Comparing equation i with the general form of a quadratic equation i.e. ax2 + bx + c = 0, we get
a = 1, b = 16, c = 39
Using factorization method (we factorize a × c i.e. 1 × 39 i.e. 39 into 2 factors such that the addition of these 2 factors gives a value that is equal to b i.e. 16)
∴ we factorize 39 into 3 and 13 (because 3 × 13 = 39 and 3 + ( 13) = 16)
x^{2}  13x  3x +39 = 0
∴ x (x  13)  3 (x  13) = 0 (Taking common factors)
∴ (x  3) (x  13) = 0
∴ either x  3 = 0 or x  13 = 0
∴ either x = 3 or x = 13
∴ the solutions of the given equation are 3 and 13
Sum of the solutions = 3 + 13 = 16
Final Answer:
Option D i.e. 16 is the correct Option.
Note:
Alternatively, formula method to solve the quadratic equation can also be used to find the solution of equation i above. Formula
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