Advertisements
Advertisements
Question
If `(1)/(2)` is a root of the equation `x^2 + kx - (5)/(4) = 0`, then the value of k is ______.
Options
2
– 2
`(1)/(4)`
`(1)/(2)`
Advertisements
Solution
If `(1)/(2)` a root of the equation `x^2 + kx - 5/4 = 0`, then the value of k is 2.
Explanation:
`(1)/(2)` is a root of the equation
x2 + kx – `(5)/(4)` = 0
Substituting the value of x = `(1)/(2)` in the equation
`(1/2)^2 + k xx (1)/(2) - (5)/(4)` = 0
⇒ `(1)/(4) + k/(2) - (5)/(4)` = 0
⇒ `k/(2) - 1` = 0
⇒ k = 1 × 2 = 2
∴ k = 2
RELATED QUESTIONS
Is the following situation possible? If so, determine their present ages. The sum of the ages of two friends is 20 years. Four years ago, the product of their ages in years was 48.
Determine the nature of the roots of the following quadratic equation:
2(a2 + b2)x2 + 2(a + b)x + 1 = 0
Find the values of k for which the roots are real and equal in each of the following equation:
(4 - k)x2 + (2k + 4)x + 8k + 1 = 0
In the following determine the set of values of k for which the given quadratic equation has real roots:
kx2 + 6x + 1 = 0
Find the value of the discriminant in the following quadratic equation :
`4 sqrt 3 "x"^2 + 5"x" - 2 sqrt 3 = 0`
Solve the following quadratic equation using formula method only
4 - 11 x = 3x2
`sqrt(3)x^2 + 10x + 7sqrt(3)` = 0
‘The sum of the ages of a boy and his sister (in years) is 25 and product of their ages is 150. Find their present ages.
If α and β be the roots of the equation x2 – 2x + 2 = 0, then the least value of n for which `(α/β)^n` = 1 is ______.
If 4 is a root of equation x2 + kx – 4 = 0; the value of k is ______.
