What is the sum of roots of the equation x^2 – 40x + 399 = 0?

Question

What is the sum of roots of the equation  x^2 – 40x + 399 = 0 ?

A. 19  
 B. 20  
 C. 21  
 D. 40  
 E. 399

PKN · Answer

Comparing the given quadratic equation with the standard form of QE, We have 
a=1 and b=-40

Sum of roots of QE=-b/a=-(-40)/1=40

Ans. (D)

Chethan92 · Answer

The general form of the quadratic equation is a x^2 +bx+c = 0.

Sum of the roots is given by  \frac{-b}{a} .

From the given equation a = 1. b = -40. c = 399.

Sum of the roots becomes =  \frac{-(-40)}{1}  = 40

D is the answer.

magbot · Answer

x^2-40x+399=0 
 x^2-40x+400-1=0 
 x^2-40x+400=1 
 (x-20)^2=1 
 (x-20)=\sqrt{1} 
 x-20=1  and  x-20=-1 
 x=21  and  x=19 
Sum of roots=21+19=40
Answer: D

MathRevolution · Answer

=>

Let  p  and  q  be the roots of the equation  x^2 – 40x + 399 = 0. 
Then  x^2 – 40x + 399 = (x-p)(x-q) = x^2 – (p+q)x + pq. 
Equating coefficients gives p + q = 40  from the coefficient of  x .

Therefore, the answer is D.
Answer: D

ScottTargetTestPrep · Answer

In a quadratic equation of the form ax^2 + bx + c = 0, the sum of the roots is -b/a. Therefore, here the sum of the roots is -(-40)/1 = 40.

Answer: D

EMPOWERMathExpert · Answer

While you could find the prime factors  399  and determine that the two roots are  19  and  21 , there is a quadratic pattern that we can use to answer this question.

The quadratic equation is given by the general form:   ax^2  +  bx  +  c   =0 , where:

a =  coefficient of  x^2  
  b =  coefficient of  x  
  c =  constant

A quadratic equation can have two roots and the sum of its roots is given by   -b   /   a  , therefore:

sum \ of \ roots = -\frac{b}{a} = - \frac{(-40)}{1} = 40

The final answer is  D .

Abhishek009 · Answer

ax^2 + bx + c=0

Sum  = -\frac{b}{a}

Hence, sum  = - \frac{-40}{1} = 40 , Answer must be (D)

What is the sum of roots of the equation x^2 – 40x + 399 = 0?

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What is the sum of roots of the equation x^2 – 40x + 399 = 0?

Prep Toolkit

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My Rewards