
What are the roots of the quadratic equation x² + 4x + 7 = 0?
Discriminant = b^2  4ac = 4^2  4(1)(7) = 16  28 = 12 < 0 As D<0, the equation has complex roots. x = 4 + v12 i / 2 = 2 + v3i x = 2  v3i These are the roots of this equation where i is...
3 hours ago

What are the roots of the quadratic equation x² + 4x + 7 = 0?
Discriminant = b^2  4ac = 4^2  4(1)(7) = 16  28 = 12 < 0 As D<0, the equation has complex roots. x = 4 + v12 i / 2 = 2 + v3i x = 2  v3i These are the roots of this equation where i is...
3 hours ago

how to prove that when ellipse and hyperbola intersect orthogonally , they are confocal.
First of all, write the equations of hyperbola and ellipse in general form. They intersect at 2 points. Take one point and write the equations of tangent to both ellipse and hyperbola at the point of...
yesterday

Find all n ? N, such that the equation x8/n10 = n/x has no solution .
We get : x^2  8x + 10n  n^2 = 0 For no roots, D<0 64  4(10nn^2) <0 64  40n + 4n^2 <0 n^2  10n + 16 < 0 (n8)(n2) < 0 n = (2,8) Hence, n can be 3,4,5,6,7 for no solution of x...
yesterday

Find all n ? N, such that the equation x8/n10 = n/x has no solution .
We get : x^2  8x + 10n  n^2 = 0 For no roots, D<0 64  4(10nn^2) <0 64  40n + 4n^2 <0 n^2  10n + 16 < 0 (n8)(n2) < 0 n = (2,8) Hence, n can be 3,4,5,6,7 for no solution of x...
yesterday

Find all real numbers A , B such that the function f (x) = A.2x + B, satisfies the...
Differentiate the function : f`(x) = 2A f`(1) = 2A = 2 Hence, A = 1 Integrate the function : Ax^2 + Bx : 0 to 3 = 7 9A + 3B = 7 9 + 3B = 7 B = 2/3 Thanks Bharat Bajaj askiitians faculty IIT Delhi
yesterday

if the mean deviation about the median of the numbers a,2a,.........,50a is 50,then IaI...
The median of this list = 25a + 26a / 2 = 25.5a Mean deviation about the median = a  25.5a + 2a  25.5a .......  50a  25.5a / 50 = 50 50(50)= 25.5a(25)  ( a + 2a... 25a) + (26a + 27a ... 50a)...
yesterday

Coefficient of x^5 in f(x) = (x+1)(x+2)..(x+6)??
Coeff. of x^5 = b Sum of roots of f(x) = b/a = 1 2  3 4 5  6 = 21 Hence, b = 21 Thanks Bharat Bajaj IIT Delhi askiitians faculty
yesterday

I would like to know if you have the direct formula to find the orthocentre, centroid,...
for orthocentre & circumcentre there is no direct formula but we can find them easily. Orthocentre intersection point of altitude so if you able to find the equation of altitude we can find...
2 days ago

I need to find the tangent line to an ellipse by only knowing the slope of a parallel line...
Equation of ellipse : x²/a² + y²/b² = 1 Let the point of tangency, whose coordinates will also satisfy the equation of the tangent line, be (p,q). The slope of the tangent line is equal to the value...
3 days ago

How to approximately draw a parabola given its equation : ax^2 + bx + c = y
First check if the roots of y are real or not from Discriminant : If D > 0, the parabola cuts the xaxis at two points If D=0, the parabola touches the xaxis If D<0, the parabola doesnt touches...
3 days ago

What is DeMoivre`s theorem in complex numbers ?
De Moivre’s Theorem : It is a formula useful for finding powers and roots of complex numbers . Say, given a complex number z, and you have to find its cube. Dont use the usual method to multiply z...
3 days ago

How to find the equation of curves which pass through the intersection of two curves whose...
For these type of questions, you have to use a parameter A to find the equation of the desired curve. If the two curves are given as f(x) and g(x), and we have to find the equation of a curve which...
3 days ago

Find A and B if the following equation if of a circle : (Ax)^2 + (B+4)y^2 + (A3)xy + 5x +...
If the equation is of circle : xy term should be zero : A3 = 0 , Hence A = 3 The coefficient of x^2 and y^2 should be equal : A^2 = B + 4 Hence, B = 5 , A = 3 Thanks Bharat Bajaj IIT Delhi askiitians...
3 days ago

What is the general equation of tangent to parabola?
Say, the general equation of parabola is : y^2 = 4ax Then , the equation of tangent to the parabola at (x1,y1) is : y.y1 = 2a(x+x1) Thanks Bharat Bajaj IIT Delhi askiitians faculty
3 days ago

How to find the equation of tangent to a circle in a short way?
general equation of circle : x^2 + y^2 + 2gx + 2fy + c = 0 If the point is given from which the tangent is drawn as (x1,y1) , the equation of tangent to this circle will be : xx1 + yy1 + g(x+x1)...
3 days ago

How to find the equation of tangent to a circle in a shortcut way? 92jadad
general equation of circle : x^2 + y^2 + 2gx + 2fy + c = 0 If the point is given from which the tangent is drawn as (x1,y1) , the equation of tangent to this circle will be : xx1 + yy1 + g(x+x1)...
3 days ago

For any curve C which is not a straight line, the distance tangent at any point P on curve...
*distance of tangent*
6 days ago

Q) In Triangle ABC, angle A =30 degrees, H is the orthocentre and D is the midpoint of BC....
Be the first one to answer
7 days ago

A and B alternatively cut Pack of Cards and Pack is shuffled after each cut.If a starts...
If B gets club first in 3rd trial, then we get: 1st trial: A doesn't get club, B doesn't get club 2nd trial: A doesn't get club, B doesn't get club 3rd trial: A doesn't get club, B gets club Without...
7 days ago

ydx + x[logy/x]dy  2xdy=0 solve using variable separable method
ydx + x[logy/x]dy  2xdy=0 ydx xdy +x[logy/x]dy xdy = 0 divide by x^2 (ydxxdy)/x^2 + (logy/x  1)/x^2 . dy = 0 d(y/x) +(logy/x1)(y/x)^2 / y^2 .dy = 0 Take y/x=z dz  (logz1)z^2/y^2 dy = 0...
7 days ago

tan ( i log (aib/a+ib) ) is equal to, in terms of a& b where i is iota.. ?
Say a = r cos C , b= r sin C where C is some angle tan C = a/b a ib/a+ib = cos C  i sin C / cos C + i sin C = ( cos c  i sin c )^ 2 = cos 2C  i sin 2C = e^(2Ci) Therefore, tan ( i log (e^(2Ci) )...
7 days ago

The maximum value of z when z satisfies the condition z + 2/z = 2 is ?
z = z +2/z  2/z <= z+2/z + 2/z or, z <= 2 + 2/z z^2  2z 2 <= 0 z^2  2z +1 <= 3 ( z  1)^2 <= 3 z  1 <= v3 Hence max. value of z is 1+v3 Thanks &...
7 days ago

what is meant by degenerated conic?
Degenerated conic: When the section of a
doublenapped right circular cone intersects with a plane a conic section is
formed. The different conic sections depend on the position of the...
9 days ago

Consider the infinite sequence {n1/n } i.e. 1 , 21/2 , 31/3 . . . . .Find the largest term...
nth term of the sequence is given by : (10n + 1)/n for n>1 Differentiate it : 0  1/n^2 It is always less than 0. Hence, it is decreasing always. Hence, the largest term is 21/2. Thanks Bharat...
10 days ago