Question

If p(x) = ax2 + bx + c and a + b + c = 0, then one zero is A) -b/a b)c/a c) b/a d) none of these *

A

B

C

D​

Answer 1

$\huge \mathfrak \pink{answer}$

Correct option is

A

(0,2)

Let f(x)=ax

2

−bx+c

Putting x=0 we get f(x)=c

and we know that c>0

therefore f(x) is positive at x=0

Now Putting x=2 we get f(x)=4a−2b+c

which can also be written as f(x)=(4a+c)−(2b)

and we know that 4a+c<2b

therefore f(x) is negative at x=2

This implies that between x=0 and x=2 there exist some value of x at which f(x)=0 which is the root of the Equation.

So a root must lie between x=0 and x=2.

In Other Options f(x) is not changing its sign in between the given values.

Therefore Answer is (A)