Question

the expression (a-2)x²+2(2a-3)x+5a-6 is for all real values of x then
express 'a'​

Answer 1

The expression is always positive that means the discriminant of the equation is always less than zero .

So, 4(2a−3)²−4(a−2)(5a−6)<0

(16a²+36−48a)−(20a²−64a+48)<0

(−4a² +16a−12)<0

(−4)(a² −4a+3)<0

(a−3)(a−1)>0

So, the expression will be positive for a>3 and a<1

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