Question

If one of the root of quadratic equation X2 + kx + 54 = 0 is -6 then

complete the following activity to find the value of ‘k’.

Activity: one of the roots of the quadratic equation X2 + kx + 54 = 0 is

-6

Therefore let’s take x =

(-6)2+ k(-6) + 54= 0

(__) -6 k + 54= 0

-6k+ = 0

k= ​

Answer 1

EXPLANATION.

One roots of the quadratic equation.

⇒ x² + kx + 54 = 0 is -6.

As we know that,

Put the value of x = -6 in equation, we get.

⇒ (-6)² + k(-6) + 54 = 0.

⇒ 36 - 6k + 54 = 0.

⇒ 90 - 6k = 0.

⇒ 6k = 90.

⇒ k = 15.

                                                                                                                             

MORE INFORMATION.

Nature of the roots of the quadratic expression.

(1) = Real and different, if b² - 4ac > 0.

(2) = Rational and different, if b² - 4ac is a perfect square.

(3) = Real and equal, if b² - 4ac = 0.

(4) = If D < 0 Roots are imaginary and unequal or complex conjugate.

Answer 2

Question:-

• If one of the root of quadratic equation x² + kx + 54 = 0 is -6 then  find the value of k.

To Find:-

• Find the value of k

Solution:-

• Let the value of x be ' -6 '

$\longrightarrow\sf \: { ( - 6 ) }^{ 2 } - 6k + 54 = 0$

$\longrightarrow\sf \: 36 - 6k + 54 = 0$

$\longrightarrow\sf \: 90 - 6k = 0$

$\longrightarrow\sf \: 6k = 90$

$\longrightarrow\sf \: k = \cancel\dfrac { 90 } { 6 }$

$\longrightarrow\sf \: k = 15$

Hence ,

• The value of k is 15