Home
Class 12
MATHS
If a ,b ,c in Ra n da b c<0 , then equa...

If `a ,b ,c in Ra n da b c<0` , then equation `b c x^2+2b+c-a)x+a=0h a s` both positive roots both negative roots real roots one positive and one negative root

A

both positive roots

B

both negatie roots

C

real roots

D

one positive and one negative root

Text Solution

Verified by Experts

The correct Answer is:
3,4
Product of roots is
`(a)/(bc) lt 0 [ because abc lt 0 ]`
Hence, roots are real and of opposite sign.
Promotional Banner

Topper's Solved these Questions

  • THEORY OF EQUATIONS

    CENGAGE|Exercise Exercise (Comprehension)|37 Videos

  • THEORY OF EQUATIONS

    CENGAGE|Exercise Exercise (Matrix)|6 Videos

  • THEORY OF EQUATIONS

    CENGAGE|Exercise Exercise (Single)|89 Videos

  • STRAIGHT LINES

    CENGAGE|Exercise JEE Advanced Previous Year|4 Videos

  • THREE DIMENSIONAL GEOMETRY

    CENGAGE|Exercise Question Bank|20 Videos

Similar Questions

Explore conceptually related problems

If a , b ,c in Ra n da(a+b)+b(b+c)+c(c+a)=0 then a.a=b=c=0 b. a+b+c+=0 c. (a-b)^2+(b-c)^2+(c-a)^2=0 d. a^3+b^3+c^3+3a b c=0

Roots of the equation |x m n1a x n1a b x1a b c1|=0 are independent of m ,a n dn independent of a ,b ,a n dc depend on m ,n ,a n da ,b ,c independent of m , na n da ,b ,c

A segment of a line P Q with its extremities on A Ba n dA C bisects a triangle A B C with sides a ,b ,c into two equal areas. Find the shortest length of the segment P Qdot

If the vectors vec a , vec b ,a n d vec c form the sides B C ,C Aa n dA B , respectively, of triangle A B C ,t h e n vec adot vec b+ vec bdot vec c+ vec cdot vec a=0 b. vec axx vec b= vec bxx vec c= vec cxx vec a c. vec adot vec b= vec bdot vec c= vec cdot vec a d. vec axx vec b+ vec bxx vec c+ vec cxx vec a=0

A ,B ,Ca n dD have position vectors vec a , vec b , vec ca n d vec d , respectively, such that vec a- vec b=2( vec d- vec c)dot Then a. A Ba n dC D bisect each other b. B Da n dA C bisect each other c. A Ba n dC D trisect each other d. B Da n dA C trisect each other

In a triangle A B C , let P a n d Q be points on A Ba n dA C respectively such that P Q || B C . Prove that the median A D bisects P Qdot

Statement 1: if a ,b ,c ,d are real numbers and A=[a b c d]a n dA^3=O ,t h e nA^2=Odot Statement 2: For matrix A=[a b c d] we have A^2=(a+d)A+(a d-b c)I=Odot

CENGAGE-THEORY OF EQUATIONS-Exercise (Multiple)
  1. If (x^(2) + 5)/(2) = x - 2 cos (m + nx) has at least one real root, ...

    Text Solution

    |

  2. Let three quadratic equations ax^(2) - 2bx + c = 0, bx^(2) - 2 cx + a...

    Text Solution

    |

  3. Consider the quadratic equation x^2 + 2(a+1)x + 9a-5 = 0 have

    Text Solution

    |

  4. If a ,b ,c in Ra n da b c<0 , then equation b c x^2+2b+c-a)x+a=0h a s...

    Text Solution

    |

  5. The graph of the quadratic trinomial u=a x^2+b x+c has its vertex at (...

    Text Solution

    |

  6. Let a ,b ,c in Q^+ satisfying a > b > cdot Which of the following sta...

    Text Solution

    |

  7. Let f(X) = ax^(2) + bx + c . Consider the following diagram .

    Text Solution

    |

  8. Graph of y = ax^(2) + bx + c is as shown in the figure . If PQ= 9, ...

    Text Solution

    |

  9. ax^2 + bx + c = 0(a > 0), has two roots alpha and beta such alpha < -2...

    Text Solution

    |

  10. If the equation ax^(2) + bx + c = 0, a,b, c, in R have non -real ro...

    Text Solution

    |

  11. If cos x - y^(2) - sqrt(y - x ^(2) - 1 )ge 0 , then

    Text Solution

    |

  12. If a x^2+(b-c)x+a-b-c=0 has unequal real roots for all c in R ,t h e ...

    Text Solution

    |

  13. If (x^2+a x+3)//(x^2+x+a) takes all real values for possible real valu...

    Text Solution

    |

  14. If the range of function f(x) = (x + 1)/(k+x^(2)) contains the inter...

    Text Solution

    |

  15. Consider equation (x - sin alpha) (x-cos alpha) - 2 = 0 . Which of the...

    Text Solution

    |

  16. If the roots of the equation, x^3 + px^2+qx-1 = 0 form an increasing G...

    Text Solution

    |

  17. Consider a quadratic equation ax^2 + bx + c = 0 having roots alpha, b...

    Text Solution

    |

  18. The equaiton ((x)/(x+1))^(2) + ((x)/(x-1))^(2) = a(a-1) has

    Text Solution

    |

  19. lf the quadratic equations x^2+bx+c=0 and bx^2+cx+1=0 have a common r...

    Text Solution

    |

  20. If the inequality cot^(2)x + (k +1) cot x - (k-3) < 0 is true for at ...

    Text Solution

    |