The number of integral values of -a- which a-a-4- x-2-3ax-2 - 0 all x belongs to real numbers is30313233

Question

Toppr Admin · Accepted Answer

A-a-x2212-4-x2-3ax-2-gt-0-x21D2-3a-2-x2212-4-xD7-2a-a-x2212-4-gt-0-x21D2-9a2-x2212-8a2-32a-gt-0-x21D2-a2-32a-gt-0-x21D2-a-a-32-gt-0Hence- number of integral -32Value of a is -30- -x2212-x221D-x2212-32-x222A-0-x221D-

The number of integral values of $^{'} a^{'}$ for which $a (a - 4) x^{2} + 3 a x + 2 > 0$ for all $x$ belongs to real numbers is
$30$
$31$
$32$
$33$

$\begin{matrix} a (a - 4) x^{2} + 3 a x + 2 > 0 \Rightarrow {(3 a)}^{2} - 4 \times 2 a (a - 4) > 0 \Rightarrow 9 a^{2} - 8 a^{2} + 32 a > 0 \Rightarrow a^{2} = 32 a > 0 \Rightarrow a (a + 32) > 0 \end{matrix}$
Hence, number of integral -32
Value of $a$ is (30) $(- \propto, - 32) \cup (0, \propto)$

The number of integral values of ′a′ for which a(a−4) x2+3ax+2>0 for all x belongs to real numbers is30313233

a(a−4)x2+3ax+2>0⇒(3a)2−4×2a(a−4)>0⇒9a2−8a2+32a>0⇒a2=32a>0⇒a(a+32)>0Hence, number of integral -32Value of a is (30) (−∝,−32)∪(0,∝)

The number of integral values of $^{'} a^{'}$ for which $a (a - 4) x^{2} + 3 a x + 2 > 0$ for all $x$ belongs to real numbers is
$30$
$31$
$32$
$33$

$\begin{matrix} a (a - 4) x^{2} + 3 a x + 2 > 0 \Rightarrow {(3 a)}^{2} - 4 \times 2 a (a - 4) > 0 \Rightarrow 9 a^{2} - 8 a^{2} + 32 a > 0 \Rightarrow a^{2} = 32 a > 0 \Rightarrow a (a + 32) > 0 \end{matrix}$
Hence, number of integral -32
Value of $a$ is (30) $(- \propto, - 32) \cup (0, \propto)$