Advertisements
Advertisements
प्रश्न
\[4 x^2 + 1 = 0\]
उत्तर
We have:
\[4 x^2 + 1 = 0\]
\[ \Rightarrow (2x )^2 - i^2 = 0\]
\[ \Rightarrow (2x )^2 - (i )^2 = 0\]
\[ \Rightarrow (2x + i) (2x - i) = 0\]
\[\Rightarrow (2x + i) = 0\] or \[(2x - i) = 0\]
\[\Rightarrow 2x = - i\] or \[2x = i\]
\[\Rightarrow\] \[x = - \frac{i}{2}\] or \[x = \frac{i}{2}\]
\[x = \frac{i}{2}\]
Hence, the roots of the equation are
APPEARS IN
संबंधित प्रश्न
Solve the equation 2x2 + x + 1 = 0
Solve the equation x2 + 3x + 5 = 0
Solve the equation `sqrt3 x^2 - sqrt2x + 3sqrt3 = 0`
Solve the equation `x^2 + x + 1/sqrt2 = 0`
Solve the equation `x^2 -2x + 3/2 = 0`
Solve the equation 27x2 – 10x + 1 = 0
x2 + 2x + 5 = 0
4x2 − 12x + 25 = 0
x2 + x + 1 = 0
\[x^2 + 2x + 5 = 0\]
\[5 x^2 - 6x + 2 = 0\]
\[21 x^2 + 9x + 1 = 0\]
\[x^2 - x + 1 = 0\]
\[x^2 + x + 1 = 0\]
\[8 x^2 - 9x + 3 = 0\]
\[x^2 - 2x + \frac{3}{2} = 0\]
\[3 x^2 - 4x + \frac{20}{3} = 0\]
Solving the following quadratic equation by factorization method:
\[x^2 + \left( 1 - 2i \right) x - 2i = 0\]
Solve the following quadratic equation:
\[x^2 + 4ix - 4 = 0\]
Solve the following quadratic equation:
\[x^2 - \left( 3\sqrt{2} - 2i \right) x - \sqrt{2} i = 0\]
Write the number of real roots of the equation \[(x - 1 )^2 + (x - 2 )^2 + (x - 3 )^2 = 0\].
If roots α, β of the equation \[x^2 - px + 16 = 0\] satisfy the relation α2 + β2 = 9, then write the value P.
If \[2 + \sqrt{3}\] is root of the equation \[x^2 + px + q = 0\] than write the values of p and q.
If a and b are roots of the equation \[x^2 - x + 1 = 0\], then write the value of a2 + b2.
Write the number of quadratic equations, with real roots, which do not change by squaring their roots.
If α, β are roots of the equation \[x^2 - a(x + 1) - c = 0\] then write the value of (1 + α) (1 + β).
The number of real roots of the equation \[( x^2 + 2x )^2 - (x + 1 )^2 - 55 = 0\] is
If α, β are the roots of the equation \[x^2 + px + 1 = 0; \gamma, \delta\] the roots of the equation \[x^2 + qx + 1 = 0, \text { then } (\alpha - \gamma)(\alpha + \delta)(\beta - \gamma)(\beta + \delta) =\]
The number of solutions of `x^2 + |x - 1| = 1` is ______.
The values of k for which the quadratic equation \[k x^2 + 1 = kx + 3x - 11 x^2\] has real and equal roots are
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
If α, β are the roots of the equation \[x^2 - p(x + 1) - c = 0, \text { then } (\alpha + 1)(\beta + 1) =\]
The least value of k which makes the roots of the equation \[x^2 + 5x + k = 0\] imaginary is
The equation of the smallest degree with real coefficients having 1 + i as one of the roots is
