Question

what is the value if K for which the quadratic equation 3x2-kx+k=0equal roots​

Answer 1

Answer :-

The value of k is 12.

Solution :-

The given equation is -

3x² - kx + k = 0

It is given in the question that this equal is having equal roots. This means that the discriminant of this equation is equal to 0.

$\tt{For \: \: a \: \: quadratic\: \: equation, }\\ \tt{a {x}^{2} + bx + c = 0} \\ \\ \mapsto \tt{Discriminant = {b}^{2} - 4ac}$

In the given equation,

a = 3,

b = -k

c = k

Discriminant of this equation (D) = (-k)² - 4 × 3 × k

=> 0 = k² - 12k

=> 12k = k²

$\tt{=> 12 = \dfrac{ {k}^{2} }{k} } \\ \\ \tt{ = > 12 = k}$

The value of k = 12

More information :-

For a quadratic equation,

ax² + bx + c = 0

Discriminant = b² - 4ac

• If the Discriminant = 0, the equation have equal roots.

• If the Discriminant < 0, the equation have no roots or imaginary roots.

• If the Discriminant > 0, the equation have two real roots.

• To find the value of x in a quadratic equation, this formula is used -

$\tt{x = \dfrac{ - (b) +\sqrt{ {b}^{2} - 4ac} }{2a} } \\\\\tt{or} \\ \\ \tt{ \dfrac{ - (b) -\sqrt{ {b}^{2} - 4ac} }{2a}}$

Answer 2

Answer:

Question⤵

➡what is the value if K for which the quadratic equation 3x2-kx+k=0equal roots.

Answer⤵

➡The value of k is 12.

Solution⤵

➡The given equation is

3x²-kx+k=0

It is given in the question that this equation having equal roots . This means that the discriminant of this equation is 0.

For the qudratic equation,

ax²+bx+c=0

➡ Discriminant= b²-4ac

In the given equation,

a=3

b=-k

c= k

Discriminant of the equation (D) =

=> (-k) ²-4×3×k=0

=> k²-12k=0

=> k²=12k

=> k²/k= 12

=> k=12

The value of k=12

More information⤵

➡For a qudratic equation,

ax²+bx+c=0

Discriminant=b²-4ac

➡If the discriminant=0, The equation has equal roots.

➡If the discriminant<0, The equation have no roots or imaginary roots.

➡If the discriminant>0, The equation have two real roots.

➡To find the value of x in a qudratic equation, this formula is used

$x = \frac{ ( - b) + \sqrt{ {b}^{2} - 4ac }}{2a} \\ \frac{ ( - b) + \sqrt{ {b}^{2} - 4ac }}{2a}$

Hope this is helpful to you!