"You are given a quadratic functionf(x)=ax2+bx+cand a linear..." solved and explained

fun9vk

Answered question

2022-03-06

You are given a quadratic function

f (x) = a x 2 + b x + c

and a linear function g(x).
The two functions intersect at

x = 0

and at also at an x with

g (x) = f (x) = 0

and where

x < 0

.
Which of the two could, for some values of a,b,c, be an expression for g(x):
1)

g (x) = b x + c

g (x) = a x + c

Deven Paul

Beginner2022-03-07Added 1 answers

Step 1
Given:

f (x) = a x^{2} + b x + c (a \neq 0)

g (x) = b x + c

for some

x = x_{1} < 0

f (x_{1}) = a x_{1}^{2} + b x_{1} + c

(1)

g (x_{1}) = b x_{1} + c

(2)
(1)-(2)

a x_{1}^{2} = 0, a = 0

, it is not allowed
So, this is not the right choice, only option is (2)

g (x) = a x + c .

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