Advertisements
Advertisements
प्रश्न
Solve the equation 27x2 – 10x + 1 = 0
उत्तर
The given quadratic equation is 27x2 – 10x + 1 = 0
On comparing the given equation with ax2 + bx + c = 0, we obtain
a = 27, b = –10, and c = 1
Therefore, the discriminant of the given equation is
D = b2 – 4ac = (–10)2 – 4 × 27 × 1 = 100 – 108 = –8
Therefore, the required solutions are
APPEARS IN
संबंधित प्रश्न
Solve the equation `3x^2 - 4x + 20/3 = 0`
9x2 + 4 = 0
4x2 − 12x + 25 = 0
\[x^2 - 4x + 7 = 0\]
\[x^2 - x + 1 = 0\]
\[27 x^2 - 10 + 1 = 0\]
\[2 x^2 + x + 1 = 0\]
\[\sqrt{3} x^2 - \sqrt{2}x + 3\sqrt{3} = 0\]
\[\sqrt{2} x^2 + x + \sqrt{2} = 0\]
\[x^2 + \frac{x}{\sqrt{2}} + 1 = 0\]
\[\sqrt{5} x^2 + x + \sqrt{5} = 0\]
\[- x^2 + x - 2 = 0\]
\[3 x^2 - 4x + \frac{20}{3} = 0\]
Solving the following quadratic equation by factorization method:
\[x^2 + \left( 1 - 2i \right) x - 2i = 0\]
Solving the following quadratic equation by factorization method:
\[x^2 - \left( 2\sqrt{3} + 3i \right) x + 6\sqrt{3}i = 0\]
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:
\[x^2 - x + \left( 1 + i \right) = 0\]
Solve the following quadratic equation:
\[i x^2 - x + 12i = 0\]
Solve the following quadratic equation:
\[x^2 - \left( \sqrt{2} + i \right) x + \sqrt{2}i = 0\]
Write the number of real roots of the equation \[(x - 1 )^2 + (x - 2 )^2 + (x - 3 )^2 = 0\].
If a and b are roots of the equation \[x^2 - px + q = 0\], than write the value of \[\frac{1}{a} + \frac{1}{b}\].
If roots α, β of the equation \[x^2 - px + 16 = 0\] satisfy the relation α2 + β2 = 9, then write the value P.
If α, β are roots of the equation \[x^2 - a(x + 1) - c = 0\] then write the value of (1 + α) (1 + β).
If a, b are the roots of the equation \[x^2 + x + 1 = 0, \text { then } a^2 + b^2 =\]
The values of x satisfying log3 \[( x^2 + 4x + 12) = 2\] are
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 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
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 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
The least value of k which makes the roots of the equation \[x^2 + 5x + k = 0\] imaginary 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.