Question

If expression x2 - mx + 1 is positive, then
(1) m2-4<0
(2) m2- 4=0
(3) m2– 4>0
(4) m=2
step by step explaination pls​

Answer 1

answer : option (1) m² - 4 < 0

explanation : expression, x² - mx + 1 > 0

then, we have to find value of m. right ?

think about the graph of x² - mx +1 > 0

it is the graph of parabolic which lies just above the x-axis but doesn't touch the x-axis because x² - mx + 1 doesn't equal to 0 it is just greater than 1.

actually, concept of a general quadratic inequality ax² + bx + c > 0 is that

a > 0 and D < 0

means, coefficient of x² > 0

and discriminant < 0

NOW for this inequality x² - mx +1 > 0

coefficient of x² = 1 > 0 it is true .

discriminant , D = (-m)² - 4 < 0

or, m² - 4 < 0

hence, only option (1) is correct.