Question

If -5 is a root of the quadratic equation 2x2 + mx = 15 and the quadratic equation
m(x2 + x) + k = 0 has equal roots, find the value of k.
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Answer 1

Answer:

Hello dear user

Here is your answer.

$given \: p(x) = 2 {x }^{2} + mx = 15 \\ and \: root \: is \: also \: given \: \alpha = - 5 \\ putting \: this \: value \: and \: get \: value \: of \: m \\ p( - 5) = 2 \times {5}^{2} + ( - 5 \times m) = 15 \\ p( - 5) = - 50 - 5m = 15 \\ p( - 5) = \frac{ - 35}{ - 5} = 7 \\ \\ now \: we \: get \: m \: value \\ putting \: in \: other \: equation$

$m( {x}^{2} + x) + k = 0 \\ 7 {x }^{2} + 7x + k = 0 \\ also \: given \: it \: has \: equal \: roots \: so \\ {b}^{2} - 4ac = 0 \\ 49 - 4 \times 7 \times k = 0 \\ k = \frac{49}{28}$

Hope it is clear to you.