Question

AP GP help @ganeshie8

Answer 1

If the quadratic equation \[ax ^{2}-2bx+c=0\] has two equal roots, which of the following are true?

Answer 2

1: both roots are b/a
2: a,b,c are GP
3. a,b,c are AP

Answer 3

Discriminant has to be 0 for a quadratic to have equal roots

Answer 4

find the discriminant of given equation and set it equal to 0

Answer 5

2b^2-4ac = 0????

Answer 6

(2b)^2 - 4ac = 0

Answer 7

cancel 4, you get

b^2 - ac = 0

b^2 = ac

b = sqrt(ac)

that means b is the geometric mean of a and c

Answer 8

that also means a, b, c are in GP

Answer 9

um what about the roots

Answer 10

yes both roots will be b/a

Answer 11

thaks

Answer 12

b/c when D = 0, quadratic formula gives :
\[x = \dfrac{2b \pm 0}{2a} \]