Question

Find the values of k so that the quadratic equation 3x² - 2kx + 12 = 0 has equal roots.​

Answer 1

${\huge{\underline{\underline{\rm{Question:-}}}}}$

Q) Find the values of k so that the Quadratic Equation 3x² - 2kx + 12 = 0 has equal roots .

${\huge{\rm{\underline{\underline{Answer\checkmark}}}}}$

☆ Given :·

• Quadratic equation : 3x² - 2kx + 12 = 0
• This equation has equal roots .

☆ To Find :·

• The value of k .

☆ Solution :·

The standard Quadratic Equation is in the form :

$\boxed{ \tt{a {x}^{2} + bx + c}}$

Compare it with given Equation :

$\tt \: a {x}^{2} + bx + c \rang \lang \: 3 {x}^{2} - 2kx + 12$

We get -

• a = 3
• b = -2k
• c = 12

Now , as we know that the Equation has equal roots so ,

The Discriminant (d) must be equal to zero (0)

Using the Formula to find discriminant -

$\boxed{ \tt{d = {b}^{2} - 4ac}}$

$\mapsto \rm \: d = {( - 2k)}^{2} - 4 \times 3 \times 12$

$\mapsto \rm \: 0 = 4 {k}^{2} - 144$

$\mapsto \rm \: 0 = 4( {k}^{2} - 36)$

$\mapsto \rm \: 0 = {k}^{2} - 36$

$\mapsto \rm \: 0 = {k}^{2} - {6}^{2}$

Using

$\boxed{ \tt \: {a}^{2} - {b}^{2} = (a + b)(a - b)}$

$\mapsto \rm \: (k + 6)(k - 6) = 0$

So ,

Either

$\rightarrow \rm \: k + 6 = 0$

$\rightarrow \underline{\boxed{\rm{ \pink{ k = - 6}}}}$

Or

$\rightarrow \rm \: k - 6 = 0$

$\rightarrow \underline{\boxed{ \rm{ \purple{k = 6}}}}$

So ,

The value of k is either 6 or -6 .

_________________________

☆ Know More :·

• If

$\sf \: d > 0 \: \: \: roots \: are \: real \: and \: distinct \: .$

• If

$\sf \: d = 0 \: \: \: roots \: are \: real \: and \: equal \: .$

• If

$\sf \: d < 0 \: \: \: roots \: are \: imaginary \: .$

• A Quadratic Equation has 2 roots or zeroes .

• Standard form of a Quadratic Equation

$\boxed{ \frak{a {x}^{2} + bx + c}}$