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Grade 12Algebra

The roots of ax²+bx+c=0, where a≠0. an coefficents are real,are non-real complex and a+c
1) 4a+c>2b

2) 4a+c<2b

3)4a+c=2b

4) none

pooja sarkar

14 Years agoGrade 12

1 Answer

Jitender Singh

12 Years ago

Ans:
Hello Student,
Please find answer to your question below

$f(x) = ax^2 + bx + c$

The roots of the equation f(x) = 0 are non-real complex.
So f(x) will not touch the real axis. Either it is above or below the real axis.
Given the condition
a + c < b
which can be interpreted as
$f(-1) = a-b+c$
f(-1) < 0
a -b + c < 0
a + c < b
So f(x) is -ve for x = -1. So it will be -ve for all x.
$f(-2) = 4a-2b+c$
f(-2) < 0
4a – 2b + c < 0
4a + c < 2b

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