Show that that the radii of the three escribed circles of a triangle are the roots of the equation `x^3-x^2(4R+r)+xs^2-rs^2=0`

The roots of the equation x^(4)-2x^(3)+x-380=0 are

The sum of roots of the equation x^2−∣2x−3∣−4=0 is

If 2 is a root of the equation x^4+2x^3-3x^2+kx-4=0 , then k=

If r_(1), r_(2), r_(3) are radii of the escribed circles of a triangle ABC and r it the radius of its incircle, then the root(s) of the equation x^(2)-r(r_(1)r_(2)+r_(2)r_(3)+r_(3)r_(1))x+(r_(1)r_(2)r_(3)-1)=0 is/are :

Find the equation whose roots are (1)/(4) times of the roots of the equation x^(2)-3x+2=0

The radii r_1, r_2,r_3 of the escribed circles of the triangle A B C are in H.P. If the area of the triangle is 24 c m^2a n d its perimeter is 24cm, then the length of its largest side is 10 (b) 9 (c) 8 (d) none of these

The radii r_(1), r_(2), r_(3) of the escribed circles of the triangle ABC are in H.P. If the area of the triangle is 24 cm^(2) and its perimeter is 24 cm, then the length of its largest side is

The equation of the circle whose one diameter is PQ, where the ordinates of P, Q are the roots of the equation x^(2)+2x-3=0 and the abscissae are the roots of the equation y^(2)+4y-12=0 is

If the system of equations lambdap+q+r=0 p+lambdaq+r=0 p+q+lambdar=0 has non trivial solution, then the value of λ can be the roots of equation x^3-3x+2=0 (2) x^3-x+2=0 x^3+4x+1=0 (4) x^2-2x+2=0

The three roots of the equation |[x,3,7],[2,x,2],[7,6,x]| =0 are