1factorize karne mai hi to prob hai............ can u plz provide a detailed solution
the eqn 8x^2 -14xy +3y^2 +10x +10y -25=0 represents adjacent sides of a ||ogram whose diagonals intersect at the points(3,2)...find the eqn of other 2 sides ,....
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5 Answers
7u factorise it to get the 2 eqns.. Let the ||gm be ABCD . suppose u got the eqn of AD and CD.. Solve them get co-ordinates of D. now Diagnols r AC and BD. u knw they intersect at (3,2). Now using the property that the diagnols bisect,u can get get co-ordinate of B since u knw D.now for the other two (A,C) . Assign the co-ordinates of ur choice. So u have 4 variables. Get the 4 eqns to solve them. 1st 2 eqns , u can get by putting them in the eqn of the line (AD, or DC ) on which they lie.now u can get the other 2 eqns by using the propery that (3,2) is the midpoint of AC too.
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21http://www.wolframalpha.com/input/?i=factorise+8x%5E2+-14xy+%2B3y%5E2+%2B10x+%2B10y+-25%3D0
7if u can't factorise by an easy method, use Sreedhar- Acharya .by getting a quadratic in form of ax2 +bx + c.
18x2-14xy-3y2=(2x-3y)(4x-y)
so, the complete polynomial to be a pair of straight line can be written as(2x-3y+a)(4x-y+b)=0
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now solve to get a and b.