Question

Find the value of k 4 x square +kx+9=0? It is similar to ax square+bx+c =0

Answer 1

Question:-

Find the value of K ,so that 4x² + kx + 9 = 0 .it is similar to ax² + bx + c = 0 .with real and equal roots .

Answer :-

→ k = +12 or -12

To find :-

→ Value of k for given condition.

Explanation :-

We have

→ 4x² + kx + 9 = 0

Because its roots are real and equal hence its discriminate will should zero .

If we have a quadratic ax² + bx + c = 0

,then its discriminate D is -

→ D = b² - 4ac

Compare the given quadratic equations

→ a = 4 , b = k and c = 9

hence ,

$\to \sf{ D = {b}^{2} - 4ac = 0} \\ \\ \to \sf{ {(k)}^{2} - 4 \times 4 \times 9} = 0\\ \\ \implies \sf{ {k}^{2} - 144 = 0 }\\ \\ \implies \sf{ {k}^{2} = 144 } \\ \\ \implies \sf{ {k}^{2} = {( \pm12)}^{2} }$

hence K = +12 or -12 .

So we have two values of k hence we got two quadratic equations .

→ 4x² -12x +9 = 0

Or

→ 4x² + 12x + 9 = 0

Answer 2

$\tt{\huge{\orange {----------- }}} S.D$

QUESTION :

Find the value of k 4 x square +kx+9=0? It is similar to ax square+bx+c =0

SOLUTION :

The given Equation has two real and equal roots .

Hence , we can state that D = 0

=> B ^ 2 = 4 A C

Given Quadratic Equation :

4 X ^ 2 + K x + 9 = 0

=> B = K

=> B ^ 2 = K ^ 2

4 A C

=> 4 × 4 × 9

=> 144

=> K ^ 2 = 144

=> K = + 12 and - 12.

Hence two values of K, + 12 and - 12 satisfy the above Equation.

Answer :

K = + 12 and - 12 .