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:
3x2 + 2x + k = 0
Find the values of k for which the given quadratic equation has real and distinct roots:
kx2 + 6x + 1 = 0
Solve the following quadratic equation using formula method only :
16x2 = 24x + 1
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`
Determine whether the given quadratic equations have equal roots and if so, find the roots:
x2 + 5x + 5 = 0
Find the value(s) of p for which the quadratic equation (2p + 1)x2 – (7p + 2)x + (7p – 3) = 0 has equal roots. Also find these roots.
If the roots of the equations ax2 + 2bx + c = 0 and `"bx"^2 - 2sqrt"ac" "x" + "b" = 0` are simultaneously real, then
Values of k for which the quadratic equation 2x2 – kx + k = 0 has equal roots is ______.
If 3 is a root of the quadratic equation x2 – px + 3 = 0 then p is equal to ______.
The roots of equation (q – r)x2 + (r – p)x + (p – q) = 0 are equal.
Prove that 2q = p + r; i.e., p, q, and r are in A.P.
