If -5 is a root of the quadratic equation $2 x^{2} + p x - 15 = 0$ and the quadratic equation $p (x^{2} + x) + k = 0$ has equal roots, find the value of k.

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Solution

Given $- 5$ is a root of the equation $2 x^{2} + p x - 15 = 0$ .
Therefore,
$2 (- 5)^{2} - 5 p - 15 = 0$
$5 p = 35$
$p = 7$

Putting $p = 7$ in $p (x^{2} + x) + k = 0$ , we get $7 x^{2} + 7 x + k = 0$

This equation will have equal roots, if
Discriminant = 0
$49 - 4 \times 7 \times k = 0$
$k = \frac{49}{28}$
$k = \frac{7}{4}$

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Similar questions

If $- 5$ is a root of the quadratic equation $2 x^{2} + p x - 15 = 0$ and the quadratic equation $p (x^{2} + x) + k = 0$ has equal roots, find the value of $k$ .

Q. If

- 5

is one root of quadratic equation

2 x^{2} + p x - 15 = 0

and roots of quadratic equation

p (x^{2} + x) + k = 0

is equal ,then find the value of

k

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

Given −5 is a root of the equation 2x2+px−15=0. Therefore,2(−5)2−5p−15=05p=35p=7Putting p=7 in p(x2+x)+k=0, we get 7x2+7x+k=0This equation will have equal roots, ifDiscriminant = 049−4×7×k=0k=4928k=74

If -5 is a root of the quadratic equation $2 x^{2} + p x - 15 = 0$ and the quadratic equation $p (x^{2} + x) + k = 0$ has equal roots, find the value of k.