RD Sharma solutions for Mathematics [English] Class 11 chapter 14 - Quadratic Equations [Latest edition]

x² + 1 = 0

9x² + 4 = 0

x² + 2x + 5 = 0

4x² − 12x + 25 = 0

x² + x + 1 = 0

\[4 x^2 + 1 = 0\]

\[x^2 - 4x + 7 = 0\]

\[x^2 + 2x + 5 = 0\]

\[5 x^2 - 6x + 2 = 0\]

\[21 x^2 + 9x + 1 = 0\]

\[x^2 - x + 1 = 0\]

\[x^2 + x + 1 = 0\]

\[17 x^2 - 8x + 1 = 0\]

\[27 x^2 - 10 + 1 = 0\]

\[17 x^2 + 28x + 12 = 0\]

\[21 x^2 - 28x + 10 = 0\]

\[8 x^2 - 9x + 3 = 0\]

\[13 x^2 + 7x + 1 = 0\]

\[2 x^2 + x + 1 = 0\]

\[\sqrt{3} x^2 - \sqrt{2}x + 3\sqrt{3} = 0\]

\[\sqrt{2} x^2 + x + \sqrt{2} = 0\]

\[x^2 + x + \frac{1}{\sqrt{2}} = 0\]

\[x^2 + \frac{x}{\sqrt{2}} + 1 = 0\]

\[\sqrt{5} x^2 + x + \sqrt{5} = 0\]

\[- x^2 + x - 2 = 0\]

\[x^2 - 2x + \frac{3}{2} = 0\]

\[3 x^2 - 4x + \frac{20}{3} = 0\]

Solving the following quadratic equation by factorization method:

\[x^2 + 10ix - 21 = 0\]

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:

\[x^2 - \left( 2\sqrt{3} + 3i \right) x + 6\sqrt{3}i = 0\]

Solving the following quadratic equation by factorization method:

\[6 x^2 - 17ix - 12 = 0\]

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:

\[\left( 2 + i \right) x^2 - \left( 5 - i \right) x + 2 \left( 1 - i \right) = 0\]

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:

\[x^2 + 4ix - 4 = 0\]

Solve the following quadratic equation:

\[2 x^2 + \sqrt{15}ix - i = 0\]

Solve the following quadratic equation:

\[x^2 - x + \left( 1 + i \right) = 0\]

Solve the following quadratic equation:

\[i x^2 - x + 12i = 0\]

Solve the following quadratic equation:

\[x^2 - \left( 3\sqrt{2} - 2i \right) x - \sqrt{2} i = 0\]

Solve the following quadratic equation:

\[x^2 - \left( \sqrt{2} + i \right) x + \sqrt{2}i = 0\]

Solve the following quadratic equation:

\[2 x^2 - \left( 3 + 7i \right) x + \left( 9i - 3 \right) = 0\]

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 \[2 + \sqrt{3}\] is root of the equation \[x^2 + px + q = 0\] than write the values of p and q.

If the difference between the roots of the equation \[x^2 + ax + 8 = 0\] is 2, write the values of a.

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 \[- \frac{1}{\alpha}\text { and } - \frac{1}{\beta}\].

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 complete set of values of k, for which the quadratic equation  \[x^2 - kx + k + 2 = 0\] has equal roots, consists of

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 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

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 \[a x^2 + bx + c = 0, \text { then } \frac{1}{a\alpha + b} + \frac{1}{a\beta + b} =\]

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 ______. 

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 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

If the difference of the roots of \[x^2 - px + q = 0\]  is unity, then

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