Question

Determine the value of ‘m’ so that the equation x

2

– 4x + (m – 4) = 0 has equal

roots​

Answer 1

The value of m so that the equation $x^2-4x+(m-4)=0$ has equal roots is 8

Step-by-step explanation:

The given quadratic equation is

$x^2-4x+(m-4)=0$

We know that discriminant of a quadratic equation $ax^2+bx+c=0$ is given by

$D=b^2-4ac$

We also know that if a quadratic equation has equal roots then its discriminant should be zero

i.e. $D=0$

Since the given quadratic equation has equal roots

Therefore,

$(-4)^2-4(m-4)=0$

$16-4m+16=0$

$4m=32$

$\implies m=8$

Hope this answer is helpful.

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Answer 2

Given:

$x^2-4x+(m-4)$

To Find:

Value of m = ?

Solution:

According to the given equation:

a = 1

b = 4

c = (m-4)

If the given having equal roots then,

⇒  $b^2-4ac=0$

On putting the estimated values, we get

⇒  $(-4)^2-4\times 1(m-4)=0$

⇒  $16-4(m-4)=0$

⇒  $16-4m+16=0$

⇒  $32-4m=0$

⇒  $4m=32$

⇒  $m=\frac{32}{4}$

⇒  $m=8$

So that the value of m will be "8".