Question

If alpha and beta are the zeros of the polynomial 2 x square + 5 x + k satisfying the relation alpha square + b square + alpha beta is equal to 21 by 4 find the value of k

Answer 1

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Here, a = 2 , b = 5 and c = k.
and we know that
$\alpha + \beta = - {b \div a}$
$\alpha \beta = c \div a$
So, alpha × beta = k/2.
So, alpha + beta = -5/2.
Now by squaring both the sides,
we get,
=>alpha^2 + beta^2 + 2 alpha beta = 25/4
=>alpha^2 + beta^2 = 25/4 - 2 alpha beta
=> alpha^2 + beta^2 = 25/4 - 2×(k/2)
=> alpha^2 + beta^2 = 25-4k/4
Now,
We have to find ,
$\alpha { }^{2} + \beta ^{2} + \alpha \beta = 21 \div 4$
=>25-4k/4 + k/2 = 21/4
=>25-4k+2k = 21
=>-2k = -4
=> k = 2
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