Question

The inequality
2x-3-x²
>0 is satisfied by
x²+x+3
(A) all values of x
(C) only positive values of x
(B) no values of x
(D) only negative values of x​

Answer 1

Hi Dude

Given that,

(2x-3-x^2)/(x^2+x+3)>0

there are two ways the quotient a/b can be>0

like a>0 , b>0

or

a<0 , b<0

then

(2x-3-x^2)>0

(x^2+x+3)>0

&

(2x-3-x^2)<0

(x^2+x+3)<0

Then x belongs to ø, R,

Then x belongs to ø

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Answer 2

Answer:

(B). no values of x

For explaination , please refer to the attachment .

Note :

★ If we consider a quadratic polynomial ,

f(x) = ax² + bx + c , then ;

• If D < 0 and a < 0 => f(x) < 0 for every

x € R .

• If D < 0 and a > 0 => f(x) > 0 for every

x € R .

• If D > 0 , then f(x) = 0 exactly at two values of x € R .

• If D = 0 , then f(x) = 0 exactly at one value of x € R .

★ If a/b > 0 , then there exist two cases ;

• a > 0 and b > 0

• a < 0 and b < 0

★ If a/b < 0 , then there exist two cases ;

• a > 0 and b < 0

• a < 0 and b > 0