If –2 is a root of the quadratic equation x2
– px + 6 = 0 and x2
+ px – k = 0 has equal roots, then the value of k
is
(1) 14 (2) 18 (3) 6 (4) 10
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4
Answer:
1) 14
Step-by-step explanation:
f(x) = x² - px + 6 = 0
g(x) = x² + px - k = 0
we know that the result of the equation should be zero when the equation x is substituted with the value and solved.
When f(-2) = 0
(-2)² - p(-2) + 6 = 0
=> 2p + 10 = 0
=> p = - 5. ------------------ [1]
when g(-2) = 0
(-2)² + (-5)(-2) - k = 0 (∵ p = -5 from [1] )
=> 4 + 10 - k = 0
=> k = 14
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