Question

The product and sum of the roots of the equation |x^2|-5|x|-24=0 are respectively​

Answer 1

Answer:

+-5

Step-by-step explanation:

actually it is a combination of 2 equations

x^2-5x-24=0   (if x>0)

here x= -8 , +3   (-8 rejected)

and,

x^2+5x-24=0  (if x<0)

here x = +8 , -3   (+8 rejected)

hence product of roots = -9

sum of roots = 0

Answer 2

Answer:

Product of the roots and Sum of the roots of the equation x^2-5x-24=0 are -24 and 5 respectively.

Step-by-step explanation:

Quadratic equation:

• A polynomial equation of second degree equation is called Quadratic equation.
• Generally it is represented as ax^2+bx+c=0
• let α and β be the two roots of the above quadratic equation then
• Sum of the roots =α+β = -b/a
• Product of roots = αβ = c/a

Given quadratic equation is

x^2-5x-24=0

compare the above equation with general quadratic equation then we have

a=1, b=-5, c=-24

then

Sum of the roots = -b/a = 5

Product of roots =c/a = -24

Another way:

Consider the equation

x^2-5x-24=0

x^2-8x+3x-24=0

x(x-8)+3(x-8)=0

(x-8)(x+3)=0

x-8=0 or x+3=0

x=8,-3 are the two roots of the given equation

let α=8, and β=-3

Sum of the roots = α+β=8-3=5

Product of the roots= αβ =(8)(-3)=-24

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