Advertisements
Advertisements
Question
If `sqrt(2)` is a root of the equation `"k"x^2 + sqrt(2x) - 4` = 0, find the value of k.
Advertisements
Solution
`"k"x^2 + sqrt(2x) - 4 = 0, x = sqrt(2)`
x = `sqrt(2)` is its solution
∴ `"k"(sqrt(2))^2 + sqrt(2) xx sqrt(2) - 4` = 0
⇒ 2k + 2 - 4 = 0
⇒ 2k - 2 = 0
⇒ 2k = 2
⇒ k = `(2)/(2)`
∴ k = 1
APPEARS IN
RELATED QUESTIONS
If ad ≠ bc, then prove that the equation (a2 + b2)x2 + 2(ac + bd)x + (c2 + d2) = 0 has no real roots.
Determine the nature of the roots of the following quadratic equation:
`3x^2-2sqrt6x+2=0`
In the following determine the set of values of k for which the given quadratic equation has real roots:
2x2 + 3x + k = 0
In the following determine the set of values of k for which the given quadratic equation has real roots:
x2 - kx + 9 = 0
Solve the following quadratic equation using formula method only
`"x"^2 - 4 sqrt 15 "x" - 4 = 0`
Form the quadratic equation whose roots are:
`2 + sqrt(5) and 2 - sqrt(5)`.
Find the values of k so that the quadratic equation (4 – k) x2 + 2 (k + 2) x + (8k + 1) = 0 has equal roots.
If the roots of px2 + qx + 2 = 0 are reciprocal of each other, then:
The equation 12x2 + 4kx + 3 = 0 has real and equal roots, if:
Values of k for which the quadratic equation 2x2 – kx + k = 0 has equal roots is ______.
