If the sum of the squares of zeroes of the polynomial 5x^2+ 3x + k is 11/25 find the value of k.
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Let a and b be zeroes of the polynomial,
then (a+b) = -3/5
ab = k/5
Now,
a²+b² = 11/25
⇒(a+b)² - 2ab = 11/25
⇒(-3/5) -2(k/5) = 11/25
⇒9/25 - 2k/5 = 11/25
⇒2k/5 = 9/25 - 11/25 = -2/25
⇒k = -1/5
then (a+b) = -3/5
ab = k/5
Now,
a²+b² = 11/25
⇒(a+b)² - 2ab = 11/25
⇒(-3/5) -2(k/5) = 11/25
⇒9/25 - 2k/5 = 11/25
⇒2k/5 = 9/25 - 11/25 = -2/25
⇒k = -1/5
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