Question

f(x) is a quadratic polynomial with f(0)=6, f(1)=1 and f(2)=0 then f(3)=

Answer 1

There U go Mate! Which Class are u in by the way !?

Answer 2

Given,

Value of the function at x = 0 is 6.

Value of the function at x = 1 is 1.

Value of the function at x = 2 is 0.

To find,

Value of the function at x = 3.

Solution,

We may utilize the following mathematical approach.

The approach for obtaining the function f(x) is as follows.

Let us assume the function f(x) to be ax² + bx + c.

Now,

∴ f (0) = 6

⇒ c = 6    (Equation 1)

∴ f (1) = 1

⇒ a + b + 6 = 1

⇒ a + b = -5    (Equation 2)

∴ f(2) = 0

⇒ 4a + 2b + 6 = 0

⇒ 4a +2b = -6    (Equation 3)

Solving equation 2 and equation 3,

∴ Equation 3 - (2)(Equation 2)

⇒ 4a + 2b - 2a - 2b = -6 - (-10)

⇒ 2a = 4

⇒ a = 2

Substituting the value of 'a' to equation 2.

⇒ a + b = -5

⇒ b = -5 - 2

       = -7

Thus, The required equation = f(x) = 2x² - 7x + 6.

As a result, f (3) = 2.9 - 7.3 +6

                          = 18 -21 + 6

                          = 24 - 21

                          = 3.

The value of the function at x = 3 is 3.