Question

Find the discriminant for the following quadratic equation. Also, determine the nature of the roots.
$2(a^2+b^2)x^2+2(a+b)x+1=0;a\ne b$

• A. D> 0; Roots are real and distinct
• B. D=0 ; Roots are real and equal
• C. D < 0 ; Roots are not real
• D. D > 0; Roots are not real

Answer 1

The correct option is C D < 0 ; Roots are not real

We have,
$2(a^2+b^2)x^2+2(a+b)x+1=0;andalsoa\ne b$

Comparing with $A{x}^2+Bx+C=0$, we get,
$A=2(a^2+b^2),B=2(a+b),C=1$

Discriminant,
$D=B^2-4AC=4(a+b{)}^2-8(a^2+b^2)$
$=4a^2+4b^2+8ab-8a^2-8b^2$
$=-(4a^2+4b^2-8ab)$
$=-4(a-b{)}^2<0$
$\Rightarrow D<0$
So, the roots are not real.
Hence, c is the correct option.