Question

write the descriminant third one ​

Answer 1

Answer:-

Your answer is 1.

Explanation:-

Given:-

• $\tt\rightarrow (x-1)(2x-1) = 0.$

To Find:-

• Discriminant of the expression.

Fomula Used:-

$\\ \tt\longrightarrow D = b^2-4ac.$

Where,

• D = Discriminant.
• a = Coefficient of x².
• b = Coefficient of x.
• c = Constant term.

Solution:-

So Let Us Convert The Given Expression In Standard Form Of Quadratic equation i.e. $\bf ax^2 + bx + c=0.$

$\\ \tt\mapsto (x - 1)(2x - 1) = 0.$

$\\ \tt\mapsto x(2x - 1) - 1(2x - 1) = 0.$

$\\ \tt\mapsto2 {x}^{2} - x - 2x + 1 = 0.$

$\\ \tt\mapsto2 {x}^{2} - 3x + 1 = 0.$

So Here,

• a = 2.
• b = -3.
• c = 1.

Therefore,

$\\ \rm\mapsto Discriminant = {b}^{2} - 4ac.$

$\\ \rm\mapsto Discriminant = { ( - 3)}^{2} - 4(2)(1).$

$\\ \rm\mapsto Discriminant = \bigg [( - 3) \times ( - 3) \bigg ] -8.$

$\\ \rm\mapsto Discriminant = 9 - 8.$

$\\ \large\mapsto \boxed{ \bf Discriminant = 1.}$

Therefore Discriminant Of The Given Expression Is 1.

More to Know:-

In a Quadratic Equation/Polynomial If,

• Discriminant is 0 then the zeroes are always real and eqaul.

• Discriminant < 0 then the zeroes are not real but imaginary.

• Discriminant > 0 then the zeroes are real but unequal.

So In This Case Zeroes Of The Equation Will Be Real But Unequal As Discriminant Is > 0.

Answer 2

1

Step-by-step explanation:

Given -

(x - 1)(2x - 1) = 0

To find -

The discriminant of the equation

Solution -

First we will simplify the equation,

(x - 1)(2x - 1) = 0

=> x (2x - 1) - 1(2x - 1) = 0

=> 2x² - x - 2x + 1 = 0

=> 2x² - 3x + 1 = 0

Now it is in the standard form of quadratic equation (ax² + bx + c = 0),

Here,

a = coefficient of x² = 2

b = coefficient of x = -3

c = 1

Discriminant = b² - 4ac

=> (-3)² - 4(2)(1)

=> 9 - 8

=> 1

Hence the value of discriminant = 1

One more thing because discriminant > 0, so the zeroes of equation will be real and unequal.

More to know :-

When,

• Discriminant > 0, the zeroes of quadratic equation will be real and unequal.
• Discriminant = 0, the zeroes of equation will be real and equal (only one zero).
• Discriminant < 0, the zeroes of the equation will be unreal (imaginary).

A quadratic equation have only two zeroes.

Sum of zeroes of quadratic equation = -b/a

Product of zeroes of quadratic equation = c/a

Formula of quadratic equation's zeroes = (- b ± √discriminant)/2a

hope it helps.