Question

Find the value of a. 2a⁴★(-⅛ab²) when a=-1;b=1;c=-1​

Answer 1

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Correct option is

D

a<−3 or a>1

y=ax2+bx+c=4a(2ax+b)2+4ac−b2

Now it is clear, y is positive when 4a is positive and 4ac−b2 is positive or b2−4ac<0

We know that the expression ax2+bx+c>0 for all x, if a>0 and b2<4ac.

Therefore, (a2−1)x2+2(a−1)x+2 is positive for all x, if

a2−1>0 and 4(a−1)2−8(a2−1)<0

⇒a2−1>0 and −4(a−1)(a+3)<0

⇒a2−1>0 and (a−1)(a+3)>0

⇒a2>1 and a<−3 or