Home
Class 12
MATHS
If a x^2+b x+c=0 has imaginary roots and...

If `a x^2+b x+c=0` has imaginary roots and `a+b+c

Text Solution

Verified by Experts

The correct Answer is:
No such a exists .
`ax(2) + bx + c = 0` has imaginary roots . Hence .
` ax^(2) + bx + c lt AA x in R, if a gt 0`
But, given
a + c `lt ` b
or ` a - b + c 0 or f (-1) lt 0`
`rArr f(x) = ax^(2) + bx + c lt 0 AA x in R`
`rArr f(-2) = 4a - 2b + c lt 0`
`rArr 4a + c lt 2b` .
Promotional Banner

Topper's Solved these Questions

  • THEORY OF EQUATIONS

    CENGAGE ENGLISH|Exercise CONCEPT APPLICATION EXERCISE 2.13|9 Videos

  • THEORY OF EQUATIONS

    CENGAGE ENGLISH|Exercise Single Correct Answer Type : Exercise|89 Videos

  • THEORY OF EQUATIONS

    CENGAGE ENGLISH|Exercise CONCEPT APPLICATION EXERCISE 2.11|8 Videos

  • STRAIGHT LINES

    CENGAGE ENGLISH|Exercise ARCHIVES (NUMERICAL VALUE TYPE)|1 Videos

  • THREE DIMENSIONAL GEOMETRY

    CENGAGE ENGLISH|Exercise All Questions|294 Videos

Similar Questions

Explore conceptually related problems

if ax^2+bx+c = 0 has imaginary roots and a+c lt b then prove that 4a+c lt 2b

If a ,b in R ,a!=0 and the quadratic equation a x^2-b x+1=0 has imaginary roots, then (a+b+1) is a. positive b. negative c. zero d. Dependent on the sign of b

Given that a x^2+b x+c=0 has no real roots and a+b+c 0 d. c=0

Given that a x^2+b x+c=0 has no real roots and a+b+c 0 d. c=0

Let f(x) = ax^(2) + bx + c, a, b, c, in R and equation f(x) - x = 0 has imaginary roots alpha, beta . If r, s be the roots of f(f(x)) - x = 0 , then |(2,alpha,delta),(beta,0,alpha),(gamma,beta,1)| is

If a, b, c are rational and the tangent to the parabola y^2 = 4kx , at P(p, q) and Q(q, b) meet at R(r, c) , then the equation ax^2 + bx-2c=0 has (A) imaginary roots (B) real and equal roots (C) rational roots (D) irrational roots

If b_1. b_2=2(c_1+c_2) then at least one of the equation x^2+b_1x+c_1=0 and x^2+b_2x+c_2=0 has a) imaginary roots b) real roots c) purely imaginary roots d) none of these

If x^2+3x+5=0a n da x^2+b x+c=0 have common root/roots and a ,b ,c in N , then find the minimum value of a+b+ c dot

If a x^2+b x+c=0 has equal roots, then c= (a) b/(2a) (b) b/(2a) (c) (-b^2)/(4a) (d) (b^2)/(4a)

If x^(2)+bx+1=0,binR has imaginary root z such that |z+1|=3 then |b| can be: