Please solve question 32 Q 32 The expression a2x2+bx+1 will be positive for all x∈R if [1] b2 4a2 - Maths - Complex Numbers and Quadratic Equations

Question

Please solve question 32 Q 32 The expression a 2 x 2 + b x + 1 will be positive for all x ∈ R if [1] b 2 > 4 a 2 [2] b 2 < 4 a 2 [3] 4 b 2 > a 2 [4] 4 b 2 < a 2

Aarushi Mishra · Accepted Answer

A quadritic polynomial fx=a'x2+b'x+c' is completely positive or negative for all x∈ℝ, if and only if its discriminant D=b'2-4a'c'<0 fx is completely positive if a'>0 and D<0, and completely negative if a'<0 and D<0Givenpx=a2x2+bx+cFor px to be always positivea'=a2>0, which is always true square of a non-zero real number is always positiveand D=b'2-4a'c'=b2-4a2c<0b2<4a2c

Please solve question 32 Q.32. The expression a 2 x 2 + b x + 1 will be positive for all x ∈ R if [1] b 2 > 4 a 2 [2] b 2 < 4 a 2 [3] 4 b 2 > a 2 [4] 4 b 2 < a 2

Please solve question 32
Q.32. The expression $a^{2} x^{2} + b x + 1$ will be positive for all $x \in R$ if
[1] $b^{2} > 4 a^{2}$
[2] $b^{2} < 4 a^{2}$
[3] $4 b^{2} > a^{2}$
[4] $4 b^{2} < a^{2}$