Question

write the discriminant of x² = 4x + c.​

Answer 1

x  

2

−4x+2=0

Here, a=1,b=−4,c=2

Therefore,

D=b  

2

−4ac=16−8=8

Answer 2

Tip

Discriminant of the equation determines the nature of roots. It tells whether the roots are distinct, equal or unreal. In a quadratic equation $ax^2+bx+c = 0$, Discriminant is given by:

$D = b^2 - 4ac$

Nature of roots conditions:

1. When $b^2 - 4ac$ is greater than 0, then the roots are real and distinct.

2.  When $b^2 - 4ac$ is equal to 0, then the roots are real and equal.

3. When $b^2 - 4ac$ is lesser than 0, then the roots are unreal (no root exists).

Step - 1

Given: $x^2 = 4x + c$.

First, let's write the given equation in standard form.

$= \: x^2 - 4x = c$

$= \: x^2 - 4x - c = 0$

Step - 2

In our standard form of equation, we can notice that:

$a = 1$

$b = -4$

$c = -c$

Step - 3

At last, its time to find the discriminant.

$D = b^2 - 4ac$

$D = (-4)^2 - (4 \times 1 \times -c)$

$D = 16 - (-4c)$

$D = 16 + 4c$

Final Answer

Hence, the discriminant of the equation is $16 + 4c$.

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