Question

If , then the equation (ax2 + bx – a) (dx2 + ex + f) = 0 (where a, b, c, d, e and f are real numbers) will have

Answer 1

Answer:

Solution:

Given a,b,c in G.P.

So b2 = ac

Hence b = √ac

ax2+2bx+c = 0

Put b = √(ac) in above equation, we get

ax2+2√(ac)x+c = 0

(√(a)x+√c)2 = 0

So x = -√(c/a)

Given equations ax2 + 2bx + c = 0 and dx2 + 2ex + f = 0 have a common root.

So x = -√(c/a) should satisfy dx2 + 2ex + f = 0.

Put x = -√(c/a) in dx2 + 2ex + f = 0.

d(c/a)-2e√(c/a) + f = 0

Divide by c, we get

(d/a) -2(e/√ca)+(f/c) = 0

Put b = √ac in above equation

(d/a)+(f/c) = 2(e/b)

So (d/a), (e/b), (f/c) are in A.P

Hence option (1) is the answer.

Step-by-step explanation: