Question

.Consider the following two curves in the X-Y plane y=(x3+x2+5) y=(x2+x+5) Which of the following statements is true for -2<= x <=2? a. The two curves do not intersect. b. The two curves intersect thrice. c. The two curves intersect twice. d. The two curves intersect once.

Answer 1

Answer:

The two curves intersect thrice.   Option B is correct

Explanation:  

We have two curves equation:

y=x³ + x² + 5

y = x² + x + 5

We equate each other.

x³ + x² + 5 = x² + x + 5

Subtract x² both the side

x³ + 5 =  x + 5

Subtract 5 both the side

x³  =  x

x³ - x = 0

x(x² - 1) = 0

x(x + 1)(x - 1) = 0

We get

x = 0    &   x - 1 = 0   & x + 1 = 0

x = 0, x = 1 & x = -1

We get the three values of x in interval [-2,2]

So, both the curves cuts each other exactly three times.