Advertisements
Advertisements
प्रश्न
Solve the equation x2 + 3x + 9 = 0
उत्तर
The given quadratic equation is x2 + 3x + 9 = 0
On comparing the given equation with ax2 + bx + c = 0, we obtain
a = 1, b = 3, and c = 9
Therefore, the discriminant of the given equation is
D = b2 – 4ac = 32 – 4 × 1 × 9 = 9 – 36 = –27
Therefore, the required solutions are
APPEARS IN
संबंधित प्रश्न
Solve the equation 27x2 – 10x + 1 = 0
4x2 − 12x + 25 = 0
\[x^2 + 2x + 5 = 0\]
\[27 x^2 - 10 + 1 = 0\]
\[17 x^2 + 28x + 12 = 0\]
\[x^2 + x + \frac{1}{\sqrt{2}} = 0\]
\[x^2 + \frac{x}{\sqrt{2}} + 1 = 0\]
\[\sqrt{5} x^2 + x + \sqrt{5} = 0\]
\[3 x^2 - 4x + \frac{20}{3} = 0\]
Solving the following quadratic equation by factorization method:
\[x^2 + 10ix - 21 = 0\]
Solve the following quadratic equation:
\[x^2 - \left( 3\sqrt{2} + 2i \right) x + 6\sqrt{2i} = 0\]
Solve the following quadratic equation:
\[x^2 + 4ix - 4 = 0\]
Solve the following quadratic equation:
\[i x^2 - x + 12i = 0\]
Solve the following quadratic equation:
\[2 x^2 - \left( 3 + 7i \right) x + \left( 9i - 3 \right) = 0\]
Write roots of the equation \[(a - b) x^2 + (b - c)x + (c - a) = 0\] .
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 \[x^2 + lx + m = 0\] , write an equation whose roots are \[- \frac{1}{\alpha}\text { and } - \frac{1}{\beta}\].
For the equation \[\left| x \right|^2 + \left| x \right| - 6 = 0\] ,the sum of the real roots is
If a, b are the roots of the equation \[x^2 + x + 1 = 0, \text { then } a^2 + b^2 =\]
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 real solutions of \[\left| 2x - x^2 - 3 \right| = 1\] is
The number of solutions of `x^2 + |x - 1| = 1` 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
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 set of all values of m for which both the roots of the equation \[x^2 - (m + 1)x + m + 4 = 0\] are real and negative, is
The number of roots of the equation \[\frac{(x + 2)(x - 5)}{(x - 3)(x + 6)} = \frac{x - 2}{x + 4}\] is
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
Find the value of P such that the difference of the roots of the equation x2 – Px + 8 = 0 is 2.
Find the value of a such that the sum of the squares of the roots of the equation x2 – (a – 2)x – (a + 1) = 0 is least.
