Advertisements
Advertisements
प्रश्न
Find the value of P such that the difference of the roots of the equation x2 – Px + 8 = 0 is 2.
उत्तर
Let α, β be the roots of the equation x2 – Px + 8 = 0
Therefore α + β = P and α . β = 8.
Now `"a" - beta = +- sqrt((alpha + beta)^2 - 4alphabeta)`
Therefore 2 = `+- sqrt("P"^2 - 32)`
⇒ P2 – 32 = 4
i.e., P = ± 6
APPEARS IN
संबंधित प्रश्न
Solve the equation x2 + 3x + 9 = 0
Solve the equation `x^2 + x/sqrt2 + 1 = 0`
Solve the equation 21x2 – 28x + 10 = 0
If z1 = 2 – i, z2 = 1 + i, find `|(z_1 + z_2 + 1)/(z_1 - z_2 + 1)|`
9x2 + 4 = 0
\[x^2 - 4x + 7 = 0\]
\[21 x^2 + 9x + 1 = 0\]
\[x^2 + x + 1 = 0\]
\[21 x^2 - 28x + 10 = 0\]
\[2 x^2 + x + 1 = 0\]
\[\sqrt{3} x^2 - \sqrt{2}x + 3\sqrt{3} = 0\]
\[\sqrt{2} x^2 + x + \sqrt{2} = 0\]
\[x^2 + \frac{x}{\sqrt{2}} + 1 = 0\]
\[- x^2 + x - 2 = 0\]
Solving the following quadratic equation by factorization method:
\[6 x^2 - 17ix - 12 = 0\]
Solve the following quadratic equation:
\[x^2 - \left( 2 + i \right) x - \left( 1 - 7i \right) = 0\]
Solve the following quadratic equation:
\[2 x^2 + \sqrt{15}ix - i = 0\]
Solve the following quadratic equation:
\[i x^2 - x + 12i = 0\]
Solve the following quadratic equation:
\[2 x^2 - \left( 3 + 7i \right) x + \left( 9i - 3 \right) = 0\]
If a and b are roots of the equation \[x^2 - x + 1 = 0\], then write the value of a2 + b2.
If α, β are roots of the equation \[4 x^2 + 3x + 7 = 0, \text { then } 1/\alpha + 1/\beta\] is equal to
The values of x satisfying log3 \[( x^2 + 4x + 12) = 2\] are
If the equations \[x^2 + 2x + 3\lambda = 0 \text { and } 2 x^2 + 3x + 5\lambda = 0\] have a non-zero common roots, then λ =
The value of p and q (p ≠ 0, q ≠ 0) for which p, q are the roots of the equation \[x^2 + px + q = 0\] are
The number of roots of the equation \[\frac{(x + 2)(x - 5)}{(x - 3)(x + 6)} = \frac{x - 2}{x + 4}\] is
If α, β are the roots of the equation \[x^2 + px + q = 0 \text { then } - \frac{1}{\alpha} + \frac{1}{\beta}\] are the roots of the equation
If the difference of the roots of \[x^2 - px + q = 0\] is unity, then
