Let A,G and H be the AM, GM and HM of two positive numbers a and b. The quadratic equation whose roots are A and H is
A
Ax2−(A2+G2)x+AG2=0
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
Ax2−(A2+H2)x+AH2=0
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
Hx2−(H2+G2)x+HG2=0
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
D
Gx2−(H2+G2)x+GH2=0
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution
The correct options are AAx2−(A2+G2)x+AG2=0 CHx2−(H2+G2)x+HG2=0 As A,G,H are A.M, G.M and H.M between a and b. Then A,G,H is in G.P such that G2=AH Now equation whose roots are A and H is x2−(A+H)x+AH=0 Substituting H=G2A, we get x2−(A+G2A)x+G2=0