Question

let alpha beta be the roots of ax2+bx+c = 0 and gamma delta are the roots of px2+qx+r = 0 and d1 and d2 are the discriminant of equation.if alpha bets gamma delta are in a.p d1 : d2 = ?
a) A2/p2 b)a2/b2 c)b2/q2 d)c2/r2​

Answer 1

Answer:

1)ax2+bx2+c=0<alpha beta.a and a+d 2)px2+bx2+c=0<gamma delta.a+2d and a+3d

a,b,g,d=a.p

a,a+d,a+2d,a+3d

Step-by-step explanation:

1)a) a+(a+d)=-b/a. =2a+d= -b/a b) a(a+d)=c/d =a(a+d)=c/a 2)a+2d+a+3d= -q/p =2a+5d= -q/p (a+2d)(a+3d)=r/p =r/4 D1=b^2-4ac D2=q^2-4pr (b^2-4ac)/(q^2-4pr)=(a^2(2a+d)^2-4a^2.a(a+d))/(p^2(2a+5d)^2-4p^2(a+2d)(a+3d)) =a^2/b^2 =(4a^2+d^2+4ad-4a^2-4ad)/(4a^2+25+20ap-4(a^2+5ad+6d^2) =(d^2)/(d^2) =a^2/p^2