Advertisements
Advertisements
प्रश्न
If α, β are the roots of the equation \[x^2 - p(x + 1) - c = 0, \text { then } (\alpha + 1)(\beta + 1) =\]
विकल्प
c
c − 1
1 − c
none of these
उत्तर
1 − c
Given equation:
\[x^2 - p(x + 1) - c = 0 \]
\[or x^2 - px - p - c = 0\]
Also
\[\alpha \text { and } \beta\] are the roots of the equation.
Sum of the roots = \[\alpha + \beta = p\]
Product of the roots = \[\alpha\beta = - (c + p)\]
\[\text { Then }, (\alpha + 1) (\beta + 1) = \alpha\beta + \alpha + \beta + 1 \]
\[ = - (c + p) + p + 1 \]
\[ = - c - p + p + 1\]
\[ = 1 - c\]
APPEARS IN
संबंधित प्रश्न
Solve the equation x2 + 3x + 9 = 0
Solve the equation `sqrt2x^2 + x + sqrt2 = 0`
Solve the equation `x^2 + x/sqrt2 + 1 = 0`
For any two complex numbers z1 and z2, prove that Re (z1z2) = Re z1 Re z2 – Imz1 Imz2
Solve the equation `x^2 -2x + 3/2 = 0`
Solve the equation 21x2 – 28x + 10 = 0
9x2 + 4 = 0
x2 + x + 1 = 0
\[4 x^2 + 1 = 0\]
\[x^2 - 4x + 7 = 0\]
\[x^2 + 2x + 5 = 0\]
\[x^2 - x + 1 = 0\]
\[x^2 + x + 1 = 0\]
\[13 x^2 + 7x + 1 = 0\]
\[\sqrt{3} x^2 - \sqrt{2}x + 3\sqrt{3} = 0\]
\[\sqrt{2} x^2 + x + \sqrt{2} = 0\]
\[x^2 - 2x + \frac{3}{2} = 0\]
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:
\[x^2 - \left( 5 - i \right) x + \left( 18 + i \right) = 0\]
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:
\[2 x^2 - \left( 3 + 7i \right) x + \left( 9i - 3 \right) = 0\]
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.
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 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
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 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 the difference of the roots of \[x^2 - px + q = 0\] is unity, then
Find the value of P such that the difference of the roots of the equation x2 – Px + 8 = 0 is 2.
If `|(z - 2)/(z + 2)| = pi/6`, then the locus of z is ______.
