Advertisements
Advertisements
प्रश्न
Solve the equation 2x2 + x + 1 = 0
उत्तर
The given quadratic equation is 2x2 + x + 1 = 0
On comparing the given equation with ax2 + bx + c = 0, we obtain
a = 2, b = 1, and c = 1
Therefore, the discriminant of the given equation is
D = b2 – 4ac = 12 – 4 × 2 × 1 = 1 – 8 = –7
Therefore, the required solutions are
APPEARS IN
संबंधित प्रश्न
Solve the equation x2 + 3x + 5 = 0
Solve the equation `sqrt2x^2 + x + sqrt2 = 0`
x2 + 1 = 0
x2 + 2x + 5 = 0
4x2 − 12x + 25 = 0
x2 + x + 1 = 0
\[x^2 - 4x + 7 = 0\]
\[27 x^2 - 10 + 1 = 0\]
\[8 x^2 - 9x + 3 = 0\]
\[\sqrt{3} x^2 - \sqrt{2}x + 3\sqrt{3} = 0\]
\[\sqrt{2} x^2 + x + \sqrt{2} = 0\]
\[x^2 + x + \frac{1}{\sqrt{2}} = 0\]
\[- x^2 + x - 2 = 0\]
\[3 x^2 - 4x + \frac{20}{3} = 0\]
Solve the following quadratic equation:
\[x^2 - \left( 3\sqrt{2} + 2i \right) x + 6\sqrt{2i} = 0\]
Solve the following quadratic equation:
\[x^2 - \left( 5 - i \right) x + \left( 18 + i \right) = 0\]
Solve the following quadratic equation:
\[x^2 - \left( 2 + i \right) x - \left( 1 - 7i \right) = 0\]
Solve the following quadratic equation:
\[i x^2 - 4 x - 4i = 0\]
Solve the following quadratic equation:
\[2 x^2 + \sqrt{15}ix - i = 0\]
Solve the following quadratic equation:
\[x^2 - x + \left( 1 + i \right) = 0\]
For the equation \[\left| x \right|^2 + \left| x \right| - 6 = 0\] ,the sum of the real roots is
If α, β are roots of the equation \[4 x^2 + 3x + 7 = 0, \text { then } 1/\alpha + 1/\beta\] is equal to
If α, β are the roots of the equation \[a x^2 + bx + c = 0, \text { then } \frac{1}{a\alpha + b} + \frac{1}{a\beta + b} =\]
If x is real and \[k = \frac{x^2 - x + 1}{x^2 + x + 1}\], then
If the roots of \[x^2 - bx + c = 0\] are two consecutive integers, then b2 − 4 c is
The value of a such that \[x^2 - 11x + a = 0 \text { and } x^2 - 14x + 2a = 0\] may have a common root 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
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 =
If one root of the equation \[x^2 + px + 12 = 0\] while the equation \[x^2 + px + q = 0\] has equal roots, the value of q is
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 and β are the roots of \[4 x^2 + 3x + 7 = 0\], then the value of \[\frac{1}{\alpha} + \frac{1}{\beta}\] is
If the difference of the roots of \[x^2 - px + q = 0\] is unity, then
The equation of the smallest degree with real coefficients having 1 + i as one of the roots is
If 1 – i, is a root of the equation x2 + ax + b = 0, where a, b ∈ R, then find the values of a and b.
If `|(z - 2)/(z + 2)| = pi/6`, then the locus of z is ______.