Questions
If the roots of the equation form an increasing G.P., where p and q are real, then
detailed solution
Correct option is A
Let the roots be a/r, a, ar, where a > 0, r > 1. Now,a/r+a+ar=−p (1)a(a/r)+a(ar)+(ar)(a/r)=q (2)(a/r)(a)(ar)=1 (3)⇒ a3=1⇒ a=1Hence, (3) is correct. From (1), putting a = 1, we get−p−3>0 ∵r+1r>2 ⇒ p<−3Hence, (2) is not correct. Also,1/r+1+r=−p (4)From (2), putting a = 1, we get1/r+r+1=q (5)From (4) and (5), we have−p=q⇒p+q=0Hence, (1) is correct. Now, as r > 1a/r=1/r<1and ar=r>1Hence, (4) is correct.Similar Questions
If the roots of the cubic, x3 + ax2 + bx + c = 0 are three consecutive positive integers, then the value of a2/(b + 1) is equal to _________.
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