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.
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2x² + px - 15 = 0
One of the two zeroes = -5
put x = -5
===> 2(-5)² + p(-5) - 15 = 0
===> 50 - 5p - 15 = 0
===> -5p = 35
===> p = 7 ...(1)
In the second equation:
☛ p(x² + x) + k = 0
On comparing,
a = p , b = p , c = k
===> b² - 4ac = 0 { because it has equal roots }
===> p² - 4pk = 0
===> 7² - 28k = 0 { from (1), p = 7 }
===> -28k = -49
===> 4k = 7
===> k = 7/4
Hence, the value of k is 7/4
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