Discriminant of the following quadratic equation is :
$(x - 1) (2 x - 1) = 0$

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Solution

$(x - 1) (2 x - 1) = 0$
$\Rightarrow$ $x (2 x - 1) - 1 (2 x - 1) = 0$
$\Rightarrow$ $2 x^{2} - x - 2 x + 1 = 0$
$\Rightarrow$ $2 x^{2} - 3 x + 1 = 0$
$\Rightarrow$ Comparing quadratic equation $2 x^{2} - 3 x + 1 = 0$ , with $a x^{2} + b x + c = 0$
$\Rightarrow$ We get, $a = 2, b = - 3, c = 1$
$\Rightarrow$ $D = b^{2} - 4 a c$
$= (- 3)^{2} - 4 (2) (1)$
$= 9 - 8$
$= 1$
$∴$ Discriminant of given quadratic equation is $1$ .

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Discriminant of the following quadratic equation is :(x−1)(2x−1)=0

(x−1)(2x−1)=0⇒ x(2x−1)−1(2x−1)=0⇒ 2x2−x−2x+1=0⇒ 2x2−3x+1=0⇒ Comparing quadratic equation 2x2−3x+1=0, with ax2+bx+c=0⇒ We get, a=2,b=−3,c=1⇒ D=b2−4ac =(−3)2−4(2)(1) =9−8 =1∴ Discriminant of given quadratic equation is 1.

Discriminant of the following quadratic equation is :
$(x - 1) (2 x - 1) = 0$