Question

for what values of k, the equation 9x²+6kx+4=0 has equal roots
​

Answer 1

Step-by-step explanation:

$\huge{\mathcal{\red{ITZ\:\:\: SWAGAT}}}$

$\huge\blue{\boxed{\boxed{HELLO\:MATE}}}$

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Answer 2

Answer:

$\pink{equal \: roots \: and \: 0}$

$\pink{b - 4ac \geqslant 0}$

$\pink{(6k)^{2} - 4(9)(4) \geqslant 0}$

$\pink{36 {k}^{2} - 36(4) \geqslant 0}$

$\pink{36( {k}^{2} - 4) = 0}$

$\pink{ {k}^{2} - 4 = 0}$

$\pink{ {k}^{2} = {2}^{2} }$

$\pink{k = + 2}$

Let us check:-

$\bold{9x^{2} + 6(2)x + 4 = 0}$

$\bold{9 {x}^{2} + 12x + 4 = 0}$

$\bold{9 {x}^{2} + 6x + 6x + 4 = 0}$

$\bold{3x(3x + 2) + 2(3x + 2) = 0}$

$\bold{(3x + 2)(3x + 2) = 0}$

$\bold{x = \frac{ - 2}{3} and \: \frac{ - 2}{3} }$

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