If α and β are zeroes of the polynomial p(x)=2x^2+5x+k satisfying the relation α^2+β^2+αβ=21/4,then find the value of k
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a= alpha (consider)
If a and ß be the roots of p(x)
Then a + ß = - 5/2
aß = k/2
Now we find firstly a²+ß² = (a+ß) ² - 2aß
= (-5/2)² - 2(k/2)
= 25/4 - k
Now, a²+ß²+aß = 25/4-k + k/2
By solving this, So. K= 25/2
If a and ß be the roots of p(x)
Then a + ß = - 5/2
aß = k/2
Now we find firstly a²+ß² = (a+ß) ² - 2aß
= (-5/2)² - 2(k/2)
= 25/4 - k
Now, a²+ß²+aß = 25/4-k + k/2
By solving this, So. K= 25/2
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