Question

Find a quadratic equation, from the equations given below, having same discriminant as $5x^2+2x+1=0$

• A. $-x^2+4x-8$
• B. $x^2+3x-7$
• C. $4x^2-5$
• D. $-2x^2-3x+6$

Answer 1

The correct option is A $-x^2+4x-8$

Given: set of quadratic equations

To find: the equation having same discriminant as $5x^2+2x+1=0$

Sol: The equation $5x^2+2x+1=0$ is of form $a{x}^2+bx+c=0$

$\therefore a=5,b=2,c=1$

The discriminant of this equation becomes

$b^2-4ac=2^2-4\left(5\right)\left(1\right)=4-20=-16$

(i) $-x^2+4x-8$ this is also of the form $a{x}^2+bx+c$

$\therefore a=-1,b=4,c=-8$

The discriminant of this equation becomes

$b^2-4ac=4^2-4(-1)(-8)=16-32=-16$

(ii) $x^2+3x-7$ this is also of the form $a{x}^2+bx+c$

$\therefore a=1,b=3,c=-7$

The discriminant of this equation becomes

$b^2-4ac=3^2-4\left(1\right)(-7)=9+28=37$

(iii) $4x^2-5⟹4x^2-0x-5$ this is also of the form $a{x}^2+bx+c$

$\therefore a=4,b=0,c=-5$

The discriminant of this equation becomes

$b^2-4ac=0^2-4\left(4\right)(-5)=0+80=80$

(iv) $-2x^2-3x+6$ this is also of the form $a{x}^2+bx+c$

$\therefore a=-2,b=-3,c=6$

The discriminant of this equation becomes

$b^2-4ac=(-3{)}^2-4(-2\left)\right(6)=9+48=57$