Advertisements
Advertisements
Question
In each of the following determine the; value of k for which the given value is a solution of the equation:
3x2 + 2kx - 3 = 0; x = `-(1)/(2)`
Advertisements
Solution
Since, x = `-(1)/(2)` is a root of the given equation 3x2 + 2kx - 3 = 0
Therefore,
`3(-1/2)^2 + 2k (-1/2)-3` = 0
⇒ `3 xx (1)/(4) - k - 3` = 0
⇒ k = `(3)/(4) - 3`
= `-(9)/(4)`
⇒ k = `-(9)/(4)`.
RELATED QUESTIONS
In the following determine the set of values of k for which the given quadratic equation has real roots:
2x2 + kx + 3 = 0
Find the value(s) of k so that the quadratic equation 3x2 − 2kx + 12 = 0 has equal roots ?
Solve the following quadratic equation using formula method only
25x2 + 30x + 7 = 0
Solve the following quadratic equation using formula method only
`"x"^2 - 4 sqrt 15 "x" - 4 = 0`
Find, using the quadratic formula, the roots of the following quadratic equations, if they exist
3x2 – 5x + 2 = 0
If x = 2 and x = 3 are roots of the equation 3x² – 2kx + 2m = 0. Find the values of k and m.
Without actually determining the roots comment upon the nature of the roots of each of the following equations:
`2sqrt(3)x^2 - 2sqrt(2)x - sqrt(3) = 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 value(s) of m for which each of the following quadratic equation has real and equal roots: (3m + 1)x2 + 2(m + 1)x + m = 0
Find the values of m so that the quadratic equation 3x2 – 5x – 2m = 0 has two distinct real roots.
