Question

The zeros of the quadratic polynomial x^2+4x+k are alpha and beta . Evaluate the value of K if 5alpha+2beta=1

Answer 1

$p(x) = {x}^{2} + 4x + k$

$zeroes \: are \: \alpha \: and \: \beta$

$\alpha + \beta = - 4 \\ \alpha = - 4 - \beta \\ \\ \alpha \beta = k$

$5 \alpha + 2 \beta = 1 \\ 5( - 4 - \beta ) + 2 \beta = 1 \\ - 20 - 5 \beta + 2 \beta = 1 \\ - 3 \beta - 20 = 1 \\ - 3 \beta = 21 \\ \beta = - 7$

$\alpha = - 4 - ( - 7) \\ \alpha = - 4 + 7 \\ \alpha = 3$

$k = 3( - 7) \\ k = - 21$

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