Suppose a, b, c are real numbers, and each of the equations `x^(2)+2ax+b^(2)=0` and `x^(2)+2bx+c^(2)=0` has two distinct real roots. Then the equation

Question

Suppose a, b, c are real numbers, and each of the equations `x^(2)+2ax+b^(2)=0` and `x^(2)+2bx+c^(2)=0` has two distinct real roots. Then the equation

Suppose a, b, c are real numbers, and each of the equations `x^(2)+2ax+b^(2)=0` and `x^(2)+2bx+c^(2)=0` has two distinct real roots. Then the equation `x^(2)+2cx+a^(2)=0` has - (A) Two distinct positive real roots (B) Two equal roots (C) One positive and one negative root (D) No real roots
A. Two distinct positive real roots
B. Two equal roots
C. One positive and one negative root
D. No real roots

Monjur Alahi

5 views

2025-01-04 04:42

1 Answers

Related Questions

Let a, b and c be non - zero real numbers such that ` int _(0)^(3) (3ax ^(2) + 2bx +c) dx = int _(1)^(3) (3ax^(2) + 2bx +c) dx` , then

2 Answers 4 Views

Let `alpha` and `beta` be roots of the equation `X^(2)-2x+A=0` and let `gamma` and `delta` be the roots of the equation `X^(2)-18x+B=0`. If `alpha lt

2 Answers 6 Views

If `a, b, c` are in `GP`, then the equations `ax^2 +2bx+c = 0` and `dx^2 +2ex+f =0` have a common root if `d/a , e/b , f/c `are in

2 Answers 6 Views

Suppose `alpha, beta` are roots of `ax^(2)+bx+c=0` and `gamma, delta` are roots of `Ax^(2)+Bx+C=0`. If `alpha,beta,gamma,delta` are in AP, then common

2 Answers 6 Views

Suppose `alpha, beta` are roots of `ax^(2)+bx+c=0` and `gamma, delta` are roots of `Ax^(2)+Bx+C=0`. If a,b,c are in GP as well as `alpha,beta, gamma,

2 Answers 4 Views

Suppose `alpha, beta` are roots of `ax^(2)+bx+c=0` and `gamma, delta` are roots of `Ax^(2)+Bx+C=0`. If `alpha,beta,gamma,delta` are in GP, then common

2 Answers 5 Views

If m is the AM of two distinct real numbers l and n `(l,ngt1)` and `G_(1),G_(2)" and "G_(3)` are three geometric means between l and n, then `G_(1)^(4

2 Answers 4 Views

Suppose, a, b, c are three distinct real numbers. Let P (x) =`((x-b)(x-c))/((a-b)(a-c))+((x-c)(x-a))/((b-c)(b-a))+((x-a)(x-b))/((c-a)(c-b))`. When sim

2 Answers 5 Views

Suppose the quadratic polynomial `p(x) = ax^2 + bx + c` has positive coefficient `a, b, c` such that `b- a=c-b`. If `p(x) = 0` has integer roots `alph

2 Answers 4 Views

The number of rational numbers exist between any two distinct rational numbers is

2 Answers 5 Views

Salim Ahmed Kawsar · Accepted Answer · 2023-02-05T15:29:48+06:00

Salim Ahmed Kawsar

Correct Answer - D
`x^(2)+2ax+b^(2)=0" "x^(2)+2bx+c^(2)=0`
`D_(1)gt0" "D_(2)gt0`
`4a^(2)+b^(2)gt0" "4b^(2)-4c^(2)gt0`
`a^(2)gtb^(2)…..(1)" "b^(2)gtc^(2)…….(2)`
From (1) and (2)
`a^(2)gtb^(2)gtc^(2)rArra^(2)gtc^(2)rArrc^(2)-a^(2)lt0`
`x^(2)+2cx+a^(2)=0`
`D=4c^(2)-4a^(2)lt0" No real roots"`

5 views Answered 2023-02-05 15:29