Home
Class 12
MATHS
The graph of the quadratic trinomial u=a...

The graph of the quadratic trinomial `u=a x^2+b x+c` has its vertex at (4, -5) and two x-intercepts, one positive and one negative. Which of the following holds good? a. `a >0` b. `b<0` c. `c<0` d. `8a=b`

A

`agt0`

B

`blt0`

C

`clt0`

D

`8a=b`

Text Solution

Verified by Experts

Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRATION & ITS APPLICATION

    RESONANCE ENGLISH|Exercise High Level Problem|26 Videos

  • EQUATIONS

    RESONANCE ENGLISH|Exercise EXERCISE-2 (PART-II: PREVIOUSLY ASKED QUESTION OF RMO) |5 Videos

Similar Questions

Explore conceptually related problems

If a,b,c,d,e are positive numbers, then which of the following holds good

The graph of a quadratic polynomial y=ax^(2)+bx+c,a,b, epsilonR is shown. Find its vertex,roots and D.

If graph of quadratic polynomial a x^2+b x+c cuts positive direction of y-axis, then what is the sign of c ?

If the graph of quadratic polynomial a x^2+b x+c cuts negative direction of y-axis, then what is the sign of c ?

If the quadratic equation a x^2+b x+c=0(a >0) has sec^2thetaa n dcos e c^2theta as its roots, then which of the following must hold good? b+c=0 b. b^2-4a cgeq0 c. ccgeq4a d. 4a+bgeq0

The roots of the quadratic equation (a + b-2c)x^2+ (2a-b-c) x + (a-2b + c) = 0 are

If the quadratic equation a x^2+b x+c=0(a >0) has sec^2thetaa n dcos e c^2theta as its roots, then which of the following must hold good? (a.) b+c=0 (b.) b^2-4a cgeq0 (c.) c ccgeq4a (d.) 4a+bgeq0

If a x^2+b x+c=0,a ,b ,c in R has no real zeros, and if c< 0 , then which of the following is true?

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

A quadratic trinomial P(x)=a x^2+b x+c is such that the equation P(x)=x has o real roots. Prove that in this case equation P(P(x))=x has no real roots either.

RESONANCE ENGLISH-DPP-QUESTION
  1. Of the members of three athletic teams in a certain school, 21 are in ...

    Text Solution

    |

  2. Find the value of a for which the sum of the squares of the roots of t...

    Text Solution

    |

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

    Text Solution

    |

  4. If a, b, c are real numbers satisfying the condition a+b+c=0 then the ...

    Text Solution

    |

  5. The quadratic equation whose roots are sec^(2)alphaand "cosec"^(2)alph...

    Text Solution

    |

  6. If h(x)=log(10)x, then the value of sum(n=1)^(89) h"("tan^(Omega)")"=

    Text Solution

    |

  7. Let f(n)=prod(r=1)^(n) sin(r), where r is in radians, then

    Text Solution

    |

  8. If a,b epsilon R and ax^(2)+bx+6=0 does not have two distinct real roo...

    Text Solution

    |

  9. Find the set of values of 'a', for which the expression y=(ax^2+6x-8...

    Text Solution

    |

  10. If every pair from among the equations x^2+px+qr=0,x^2+qx+rp=0 and x...

    Text Solution

    |

  11. Find a and b so that x^3+ax^2+11x+6 and x^3+bx^2+14x+8 may have one co...

    Text Solution

    |

  12. If alpha , beta are the roots of the quadratic equation (p^2 + p +...

    Text Solution

    |

  13. The roots alpha and beta of a quadratic equation are the square of two...

    Text Solution

    |

  14. The number of values of x in the in interval [0,5pi] satisfying the eq...

    Text Solution

    |

  15. If 2cos^2(pi+x)+3 sin(pi+x) vanishes then the values of x lying in the...

    Text Solution

    |

  16. ax^2+2bx-3c=0 has no real root and a+bgt3c/4 then

    Text Solution

    |

  17. The value of x satisfying the equation cos(lnx)=0, is (A) e^(pi//2) (...

    Text Solution

    |

  18. The value of the expression ((sin3theta)/sin theta)^2-((cos3theta)/cos...

    Text Solution

    |

  19. Find the smallest positive integral values of a for which the greater ...

    Text Solution

    |

  20. The set of values of 'c' for which the equation x^(2)-4x-c-sqrt(8x^(2)...

    Text Solution

    |