Question

If -5 is a root of quadratic equation 2x² + px- 15 = 0 and the quadratic equation
P(x² +x) +k = 0 has equal roots find value of k.



No one should answer except mysticd sir only​

Answer 1

$Given \: -5 \: is \: a \: root \:of \: Quadratic\\equation \: 2x^{2}+px-15=0$

/* put x = -5 in the equation, we get */

$\implies 2(-5)^{2} + p(-5) - 15 = 0$

$\implies 50 - 5p - 15 = 0$

$\implies 35 - 5p = 0$

$\implies -5p = -35$

$\implies p = \frac{-35}{-5}$

$\implies p = 7\: --(1)$

$Given \: p(x^{2}+x)+k = 0$

$\implies 7(x^{2} + x) + k = 0\: [ From \: (1) ]$

$\implies 7x^{2} + 7x+ k = 0$

/* Compare this with ax²+bx+c=0 , we get */

$a = 7 , b = 7 , c = k$

$Discreminant (D) = 0$

$\blue { ( Roots \: are \: equal ) }$

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

$\implies 7^{2} - 4 \times 7 \times k = 0$

$\implies 49 - 28k = 0$

$\implies - 28k = -49$

$\implies k = \frac{-49}{-28}$

$\implies k = \frac{7}{4}$

Therefore.,

$\red{ Value \: of \: k }\green { = \frac{7}{4}}$

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