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
Solve for x: `1/(x+1)+2/(x+2)=4/(x+4), `x ≠ -1, -2, -3
Find the value of p, for which one root of the quadratic equation px2 – 14x + 8 = 0 is 6 times the other.
Form the quadratic equation if its roots are –3 and 4.
If (k – 3), (2k + l) and (4k + 3) are three consecutive terms of an A.P., find the value of k.
Find the values of k for which the roots are real and equal in each of the following equation:
4x2 - 3kx + 1 = 0
Solve for x :
x2 + 5x − (a2 + a − 6) = 0
Solve the following quadratic equation using formula method only :
`2x + 5 sqrt 3x +6= 0 `
Solve the following quadratic equation using formula method only
16x2 - 24x = 1
Solve the following quadratic equation using formula method only
`"x"^2 + 1/2 "x" = 3`
Find the value(s) of k for which the pair of equations
kx + 2y = 3
3x + 6y = 10 has a unique solution.
`sqrt(3)x^2 + 10x + 7sqrt(3)` = 0
Find the value of k for which the following equation has equal roots:
(k − 12)x2 + 2(k − 12)x + 2 = 0.
In each of the following, determine whether the given numbers are roots of the given equations or not; 3x2 – 13x – 10 = 0; 5, `(-2)/(3)`
Find the discriminant of the following equations and hence find the nature of roots: 7x2 + 8x + 2 = 0
Discuss the nature of the roots of the following quadratic equations : `x^2 - (1)/(2)x + 4` = 0
Find the least positive value of k for which the equation x2 + kx + 4 = 0 has real roots.
Choose the correct answer from the given four options :
The value(s) of k for which the quadratic equation 2x² – kx + k = 0 has equal roots is (are)
Find the value(s) of k for which each of the following quadratic equation has equal roots: (k + 4)x2 + (k + 1)x + 1 =0 Also, find the roots for that value (s) of k in each case.
The roots of the quadratic equation `"x" + 1/"x" = 3`, x ≠ 0 are:
If the equation x2 – (2 + m)x + (–m2 – 4m – 4) = 0 has coincident roots, then:
State whether the following quadratic equation have two distinct real roots. Justify your answer.
`2x^2 - 6x + 9/2 = 0`
Every quadratic equation has exactly one root.
Find the roots of the quadratic equation by using the quadratic formula in the following:
–3x2 + 5x + 12 = 0
State whether the following quadratic equation have two distinct real roots. Justify your answer.
`sqrt(2)x^2 - 3/sqrt(2)x + 1/sqrt(2) = 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.
The probability of selecting integers a ∈ [–5, 30] such that x2 + 2(a + 4)x – 5a + 64 > 0, for all x ∈ R, is ______.
The sum of all integral values of k(k ≠ 0) for which the equation `2/(x - 1), 1/(x - 2) = 2/k` in x has no real roots, is ______.
If α, β are roots of the equation x2 + px – q = 0 and γ, δ are roots of x2 + px + r = 0, then the value of (α – y)(α – δ) is ______.
The nature of roots of the quadratic equation 9x2 – 6x – 2 = 0 is ______.
