Advertisements
Advertisements
प्रश्न
Form the quadratic equation whose roots are:
`sqrt(3) and 3sqrt(3)`
Advertisements
उत्तर
Let a, β be the roots of the required quadratic equation:
Then, a = `sqrt(3) and beta = 3sqrt(3)`
a + β = `sqrt(3) + 3sqrt(3) and abeta = sqrt(3) xx 3sqrt(3)`
∴ a + β = `4sqrt(3) and abeta = 9`
Required quadratic equation
x2 - (a + β)x + aβ = 0
⇒ x2 - 4`sqrt(3)x + 9 = 0`.
संबंधित प्रश्न
In the following determine the set of values of k for which the given quadratic equation has real roots:
2x2 + kx + 3 = 0
In the following determine the set of values of k for which the given quadratic equation has real roots:
3x2 + 2x + k = 0
Determine whether the given quadratic equations have equal roots and if so, find the roots:
x2 + 2x + 4 = 0
Choose the correct answer from the given four options :
If the equation {k + 1)x² – 2(k – 1)x + 1 = 0 has equal roots, then the values of k are
Find whether the following equation have real roots. If real roots exist, find them.
`x^2 + 5sqrt(5)x - 70 = 0`
Let α and β be the roots of the equation, 5x2 + 6x – 2 = 0. If Sn = αn + βn, n = 1, 2, 3, ....., then ______.
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 ______.
The roots of quadratic equation x2 – 1 = 0 are ______.
If the roots of x2 – px + 4 = 0 are equal, the value (values) of p is ______.
If the quadratic equation kx2 + kx + 1 = 0 has real and distinct roots, the value of k is ______.
