Question

यदि वर्ग समीकरण 9x²-Kx+16=0 के मूल समान है तो K का मान ग्यात कीजिए​

Answer 1

$Compare\: given \\quadratic \: equation: \\ 9x^{2}+Kx + 16 = 0 \: with\\ax^{2} + bx + c = 0<strong> </strong><strong>,</strong><strong> </strong>we\: get$

$a = 9 , b = -K \:and \:c = 16$

$Discreminant (D) = 0$

$\blue{( \because roots \: are \: equal )}$

$\implies b^{2} - 4ac = 0$

$\implies (-K)^{2} - 4 \times 9 \times 16 = 0$

$\implies K^{2} = 4 \times 9 \times 16$

$\implies K =\pm \sqrt{2^{2} \times 3^{2} \times 4^{2}}$

$\implies K =\pm ( 2 \times 3 \times 4)$

$\implies K = \pm 24$

Therefore.,

$\red{ Value \: of \: K } \green { = \pm 24}$

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