For which value of a is the expression x^2 - | vedclass

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(A) For the quadratic expression $f(x) = x^2 - ax + (1 - 2a^2)$ to be always positive for all real $x$,the coefficient of $x^2$ must be positive (whic

Vedclass · Accepted Answer

$ - \frac{2}{3} < a < \frac{2}{3} $

Vedclass · Answer

(A) For the quadratic expression $f(x) = x^2 - ax + (1 - 2a^2)$ to be always positive for all real $x$,the coefficient of $x^2$ must be positive (which is $1 > 0$,true) and the discriminant $D$ must be less than $0$.The discriminant $D = b^2 - 4ac = (-a)^2 - 4(1)(1 - 2a^2)$.Setting $D $a^2 - 4(1 - 2a^2) $a^2 - 4 + 8a^2 $9a^2 - 4 Factoring the expression:$(3a - 2)(3a + 2) Solving the inequality,we get:$ - \frac{2}{3} < a < \frac{2}{3} $

For which value of $a$ is the expression $x^2 - ax + 1 - 2a^2$ always positive for all real values of $x$?

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