Question

If 1/2 is the root of the equation x2 +kx-5/4=0 .find the value of k

Answer 1

let other root be α
so by equation
product of roots
$(1 \div 2)( \alpha ) = - 5 \div 4 \\ \alpha = - 5 \div 2$
Now sum of roots
$(1 \div 2) + ( - 5 \div 4) = - k \\ - 3 \div 4 = - k \\ k = 3 \div 4$
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Answer 2

x² + kx - (5/4) = 0

½ is the root of the equation.
x = ½

(½)² + k(½) - (5/4) = 0
(1/4) + k/2 - 5/4 = 0
k/2 = 5/4 - 1/4
k/2 = (5-1)/4
k/2 = 4/4
k/2 = 1
k = 2