Question

If 1/2 is a root of the equation x²+ kx – (5/4) = 0 then the value of k is

Answer 1

Answer:

$\boxed{k=2}$

Step-by-step explanation:

$given \ quadratic \ equation,\\ x^2+kx-\frac{5}{4}=0 \\\\ \frac{1}{2} \ is \ a \ root \ of \ the \ equation. \\\\ put \ x=\frac{1}{2} \\\\ => (\frac{1}{2})^2+k(\frac{1}{2})-\frac{5}{4}=0 \\\\ =>\frac{1}{4}+\frac{k}{2}=\frac{5}{4} \\\\ => \frac{k}{2}=\frac{5}{4}-\frac{1}{4} \\\\ => \frac{k}{2}=\frac{4}{4} \\\\ => \frac{k}{2}=1 \\\\ =>k=2$

Answer 2

Given 1/2 is a root

Hence substitute value of x is 1/2

(1/2)^2+k×1/2-5/4=0

1/4+k/2-5/4=0

1/4 +k/2=5/4

k/2 = 5/4-1/4

k/2 = 1

k=2