Question 25
If one root of quadratic equation $$2x^{2} - 3x + (2k + 1) = 0$$ is five times the other then the value of k is :
Solution
Let us assume the roots to be A and 5A.
Sum of roots = -b/a = 3/2
A + 5A = $$\frac{3}{2}$$ ==> A = $$\frac{1}{4}$$.
Product of roots = c/a = $$\frac{\left(2k+1\right)}{2}=k\ +\ \frac{1}{2}$$
$$A\cdot5A=k\ +\ \frac{1}{2}$$
$$\frac{1}{4}\times\ \frac{5}{4}=k\ +\ \frac{1}{2}$$
k = $$-\frac{3}{16}$$
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