9x^(2)-8x-2=0

Find the centre eccentricity, foci, directrices and length of the lotus rectum of the hyperbolas. 4x^(2)-9y^(2)-8x-32=0

Find the eccentricity, length of latus rectum, centre, foci, vertices and the equatioin to the dircctriccs of the hyperola. (i) 4x^(2)-5y^(2)-16x+10y+31=0 (ii) 5x^(2)-4y^(2)+20x+8y-4=0 (iii) 4(y+3)^(2)-9(x-2)^(2)=1 (iv) 4x^(2)-9y^(2)-8x-32=0

x^(4)+8x^(3)+9x^(2)-8x-10=0 Solve for x

If x_(1),y_(1), are the roots of x^(2)+8x-20=0,x_(2),y_(2), are the roots of 4x^(2)+32x-57=0 and x_(3),y_(3), are the roots of 9x^(2)+72x-112=0, then the points,(x_(1),y_(1)),(x_(2),y_(2)) and (x_(3),y_(3)) -

If alpha,beta are the roots of x^(2)+2x+5= (then the equation whose roots are (alpha+1)/(alpha),(beta+1)/(beta) is (A) 5x^(2)-9x+4=0 (B) 5x^(2)-8x+4=0 (C) 5x^(2)-10x+4=0 (D) 5x^(2)+9x+4=0

If x= 3+ 3^(1//3)+ 3^(2//3) , then the value of the expression x^(3)-9x^(2)+8x-12 is equal to _____

If x=9 is the chord of contact of the hyperbola x^(2)-y^(2)=9 then the equation of the corresponding pair of tangents is (A)9x^(2)-8y^(2)+18x-9=0(B)9x^(2)-8y^(2)-18x+9=0(C)9x^(2)-8y^(2)-18x-9=0(D)9x^(^^)2-8y^(^^)2+18x+9=0'

If x=9 is the chord of contact of tangents of x^(2)-y^(2)=9 , then show that the equation of corresponding tangents is 9x^(2)-8y^(2)-18x+9=0

Solve the following quadratic: 8x^(2)-9x+3=0

Without solving , comment upon the nature of roots of each of the following equations : (i) 7x^(2)-9x+2=0 (ii) 6x^(2)-13x+4=0 (iii) 25x^(2)-10x+1=0 (iv) x^(2)+2sqrt(3)x-9=0 (v) x^(2)-ax-b^(2)=0 (vi) 2x^(2)+8x+9=0