" 10."x^(2)-4x-1=0

Determine the nature of the roots of the following quadratic equations: 2x^(2)+x-1=0x^(2)-4x+4=0x^(2)+x+1=04x^(2)-4x+1=02x^(2)+5x+5=0

If alpha,beta are the roots of the equation 2x^(2)+4x-5=0, the equation whose roots are the reciprocals of 2 alpha-3 and 2 beta-3 is - (i) x^(2)+10x-11=0 (ii) 11x^(2)+10x+1=0 (ii) x^(2)+10x+11=0 (iv) 11x^(2)-10x+1=0

Axis of the parabola x ^(2) -4x-3y+10=0 is

Axis of the parabola x ^(2) -4x-3y+10=0 is

Determine the nature of the roots of the following quadratic equations: 2x^2+x-1=0 x^2-4x+4=0 x^2+x+1=0 4x^2-4x+1=0 2x^2+5x+5=0

Let f:RtoR be given by f(x)={{:(x^(5)+5x^(4)+10x^(3)+3x+1,xlt 0),(x^(2)-x+1,0 le x lt1),((2//3)x^(3)-4x^(2)+7x-(8//3),1 le x lt3),((x-2)ln(x-2)-x+(10//3),x ge 3):} Then which of the following options is/are correct?

alpha, beta are roots of quadratic equation such that alpha+beta=-4 and alpha beta=-1 , then required equation is……….a) x^2-4x-1=0 b) x^2+4x-1=0 c) x^2+4x+1=0 d) x^2-4x+1=0