Home
Class 12
MATHS
If f(x) = a + bx + cx^(2) where c > 0 an...

If `f(x) = a + bx + cx^(2)` where c > 0 and `b^(2) - 4ac < 0`. Then the area enclosed by the coordinate axes,the line x = 2 and the curve y = f(x) is given by

A

`(1)/(3) { 4f (1) + f(2)}`

B

`(1)/(2) {f(0) + 4f(1)}`

C

`(1)/(2) {f(0) + 41 f(1) + f(2)}`

D

`(1)/(3) {f(0) + 4 f(1) + f(2)}`

Text Solution

AI Generated Solution

The correct Answer is:
To find the area enclosed by the coordinate axes, the line \( x = 2 \), and the curve \( y = f(x) = a + bx + cx^2 \), where \( c > 0 \) and \( b^2 - 4ac < 0 \), we will follow these steps: ### Step 1: Calculate \( f(0) \), \( f(1) \), and \( f(2) \) 1. **Calculate \( f(0) \)**: \[ f(0) = a + b \cdot 0 + c \cdot 0^2 = a \] 2. **Calculate \( f(1) \)**: \[ f(1) = a + b \cdot 1 + c \cdot 1^2 = a + b + c \] 3. **Calculate \( f(2) \)**: \[ f(2) = a + b \cdot 2 + c \cdot 2^2 = a + 2b + 4c \]
Promotional Banner

Similar Questions

Explore conceptually related problems

If f(x) = a + bx + cx^2 where a, b, c in R then int_o ^1 f(x)dx

Let f(x)=ax^(2)+bx + c , where a in R^(+) and b^(2)-4ac lt 0 . Area bounded by y = f(x) , x-axis and the lines x = 0, x = 1, is equal to :

Let f(x) = ax^(2) - bx + c^(2), b ne 0 and f(x) ne 0 for all x in R . Then

The domain of f(x)=ln(a x^3+(a+b)x^2+(b+c)x+c), where a >0, b^2-4ac=0 , is

Let f(x) = a x^2 + bx + c , where a, b, c in R, a!=0 . Suppose |f(x)| leq1, x in [0,1] , then

Let f:[0,5] -> [0,5) be an invertible function defined by f(x) = ax^2 + bx + C, where a, b, c in R, abc != 0, then one of the root of the equation cx^2 + bx + a = 0 is:

Let f:[0,5] -> [0,5) be an invertible function defined by f(x) = ax^2 + bx + C, where a, b, c in R, abc != 0, then one of the root of the equation cx^2 + bx + a = 0 is:

If C (x) = a + bx + cx^2 , Verify that (d)/(dx) (AC) = (1)/(x) (MC - AC)

Using properties of determinant, If f(x)= a + bx + cx^(2) , prove that |(a,b,c),(b,c,a),(c,a,b)|= -f(1)f(omega)f(omega^(2)), omega is a cube root of unity

If a, b, c are positive real numbers such that the equations ax^(2) + bx + c = 0 and bx^(2) + cx + a = 0 , have a common root, then