Question

Determine the nature of roots of the following quadratic equations.
(1) x² – 4x + 4 = 0
(2) 2y² – 7y +2 = 0
(3) m² + 2m + 9 = 0

Answer 1

(1) x² – 4x + 4 = 0
Comparing the given equation with the quadratic equation $a{x}^2+bx+c=0$,
$a=1,b=-4,c=4$
Discriminant, $△=b^2-4ac={\left(-4\right)}^2-4\times 1\times 4=16-16=0$
Since the discriminant = 0 so, the roots of the given quadratic equation are real and equal.

(2) 2y² – 7y +2 = 0
Comparing the given equation with the quadratic equation $a{x}^2+bx+c=0$,
$a=2,b=-7,c=2$
Discriminant, $△=b^2-4ac={\left(-7\right)}^2-4\times 2\times 2=49-16=33$
Since the discriminant > 0 so, the roots of the given quadratic equation are real and unequal.

(3) m² + 2m + 9 = 0
Comparing the given equation with the quadratic equation $a{x}^2+bx+c=0$,
$a=1,b=2,c=9$
Discriminant, $△=b^2-4ac={\left(2\right)}^2-4\times 1\times 9=4-36=-32$
Since the discriminant < 0 so, the roots of the given quadratic equation are not real.