Question

find 'm Solkar equation
x²+2 (m+2) x+qm=0 will have equal roots?​

Answer 1

Step-by-step explanation:

Given,

${x}^{2} + 2(m + 2)x + qm = 0$

Since, it has equal roots, so its discriminant will be =0,

Here, a=1, b=2(m+2), c=qm

Now,

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

$= {(2(m + 2))}^{2} + 4(1)(qm) = 0$

$= 4(m + 2)^{2} - 4qm = 0$

$= (m + 2)^{2} - qm = 0$

${m}^{2} + 4m + 4 - qm = 0$

$= {m}^{2} + (4 - q)m + 4 = 0$

$= m = \frac{(q - 4) + \sqrt{(4 - q) ^{2} - 4(4)(1) } }{2} \: \: or \: \: m = \frac{(q - 4) - \sqrt{(4 - q) ^{2} - 4(4)(1) } }{2}$

$m = \frac{(q - 4) + \sqrt{16 + {q}^{2} - 8q - 16 } }{2} \: \: or \: \: m = \frac{(q - 4) - \sqrt{16 + {q}^{2} - 8q - 16 } }{2}$

$m = \frac{(q - 4) + \sqrt{ {q}^{2} - 8q } }{2} \: \: or \: \: m = \frac{(q - 4) - \sqrt{ {q}^{2} - 8q } }{2}$