Question

The roots of the following quadratic equation are Not real
2$(a^2+b^2)x^2$ + 2(a + b) x + 1 = 0

• A. True
• B. False

Answer 1

The correct option is A True

$2(a^2+b^2)x^2+2(a+b)x+1=0$

$\Rightarrow$ Here, $A=2(a^2+b^2),B=2(a+b),C=1$

$\Rightarrow$ $B^2-4AC$

$\Rightarrow$ $\left[2\right(a+b){]}^2-4[2(a^2+b^2)\left]\right(1)$

$\Rightarrow$ $4(a^2+2ab+b^2)-4(2a^2+2b^2)$

$\Rightarrow$ $4a^2+8ab+4b^2-8a^2-8b^2$

$\Rightarrow$ $-4a^2-4b^2+8ab$

$\Rightarrow$ $-4(a^2+b^2-2ab)$

$\Rightarrow$ $-4(a-b{)}^2$

$\Rightarrow$ Here $Discriminant$ is negative.

$\Rightarrow$ $D<0$

$\therefore$ The equation has no real roots