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

-5 is a root of quadratic equation 2x² + px - 15 = 0
so, 2(-5)² + p(-5) - 15 = 0
=> 50 - 5p - 15 = 0
=> 35 - 5p = 0
p = 7

now, put p = 7 in second quadratic equation,
p(x² + x ) + k = 0
=> 7(x² + x ) + k = 0
=> 7x² + 7x + k = 0
above equation has equal roots
so, D = b² - 4ac = 0
=> 7² - 4 × 7 × k = 0
=> 7 - 4k = 0
=> k = 7/4 = 1.75

hence, the value of k = 1.75

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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.

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.