Home
Class 12
MATHS
For what positive vavlue of n are the ze...

For what positive vavlue of n are the zeros of `p(x) = 5x^(2) + nx + 12 ` in ratio 2:3 ?

A

0.42

B

1.32

C

4.56

D

15.8

Text Solution

Verified by Experts

The correct Answer is:
D
If the zeroes of P(x) are in the ratio 2:3 they must take the form 2k and 3k for some value k, and `(x-2k)(x-3k)=x^(2)-5k+6k^(2)=0` . Dividing P(x) by 5 and equating coefficients yields `(n)/(5)=-5k` and `(12)/(5)=6k^(2)` . Therefore `, k=pmsqrt((2)/(5))` . Since the problem asks for a positive value of n, we use `k=-sqrt((2)/(5))`, so n=-25k `~~15.8`
Promotional Banner

Topper's Solved these Questions

  • MODEL TEST 5

    ENGLISH SAT|Exercise MCQs|50 Videos

  • PARAMETRIC EQUATIONS

    ENGLISH SAT|Exercise EXERCISES|3 Videos

Similar Questions

Explore conceptually related problems

For which values of a and b , the zeroes of q(x) = x^(3)+2x^(2)+a are also the zeroes of the polynomial p(x) = x^(5)-x^(4)-4x^(3)+3x^(2)+3x +b ? Which zeores of p(x) are not the zeroes of q(x) ?

For which values of a and b are zeroes of q(X) =x^(3)+2x+a also zeroes of the polynomial p(x) =x^(5)-x^(4)-4x^(3)+3x^(2)+3x+b ? Which zeroes of p(x) are not zeroes of p(x)?

If a, a_1 ,a_2----a_(2n-1),b are in A.P and a,b_1,b_2-----b_(2n-1),b are in G.P and a,c_1,c_2----c_(2n-1),b are in H.P (which are non-zero and a,b are positive real numbers), then the roots of the equation a_nx^2-b_nx |c_n=0 are (a) real and unequal (b) real and equal (c) imaginary (d) none of these

The quadratic polynomial p(x) ha following properties p(x) can be positive or zero for all real numbers p(1)=0a n dp(2)=2. Then find the quadratic polynomial.

The distance of point P(x, y) from the points A(1, -3) and B(-2, 2) are in the ratio 2 : 3. Show that 5x^(2) + 5y^(2) - 34x + 70y + 58 = 0 .

Zero of the polynomial p(x) =2x+5 is

If p = (x^(a+ b))/(x^b) , what is the value of positive integer p? (1) x = 5 (2) a = 0

If x is a positive integers and x+12=x^(2) , what is the value of x?

If alpha and beta are the zeros of the quadratic polynomial p(x)=4x^2-5x-1 , find the value of alpha^2beta+alphabeta^2 .

If a, a_1 ,a_2----a_(2n-1),b are in A.P and a,b_1,b_2-----b_(2n-1),b are in G.P and a,c_1,c_2----c_(2n-1),b are in H.P (which are non-zero and a,b are positive real numbers), then the roots of the equation a_nx^2-b_nx +c_n=0 are

ENGLISH SAT-MODEL TEST 6-MCQS
  1. In triangleABC, angleA = 45^(@) , angleB = 30^(@) , and b=8. Side a =

    Text Solution

    |

  2. The equations of the asymptotes of the graph of 4x^(2)-9y^(2) = 36 are

    Text Solution

    |

  3. If g(x-1) = x^(2)+2 , then g(x)=

    Text Solution

    |

  4. If f(x)=3x^(3)-2x^(2)+x-2 , and i =sqrt(-1) then f(i) =

    Text Solution

    |

  5. If the hour hand of a clock moves K radians in 48 minutes , K=

    Text Solution

    |

  6. If the longer diagonal of a rhombus is 10 and the large angle is 100^(...

    Text Solution

    |

  7. Let f(x)=sqrt(x^(2)-4x) and g(x) = 3x . The sum of all values for whic...

    Text Solution

    |

  8. How many subsets does a set with n distinct elements have ?

    Text Solution

    |

  9. If f(x)=2^(3x-5) , find f^(-1)(16)

    Text Solution

    |

  10. For what positive vavlue of n are the zeros of p(x) = 5x^(2) + nx + 12...

    Text Solution

    |

  11. If f(-x) = -f(x) for all x and if the point (-2,3) is on the graph of ...

    Text Solution

    |

  12. A man piles 150 tookpicks in layers so that each layer has one less to...

    Text Solution

    |

  13. If the circle x^(2)+y^(2)-2x-6y = r^(2)-10 is tangent to the line 12y ...

    Text Solution

    |

  14. If a(0) = 0.4 and a(n+1) = 2|a(n)|-1 , then a(5) =

    Text Solution

    |

  15. If 5.21^(p) = 2.86^(q) , what is the value of p/q ?

    Text Solution

    |

  16. The matrix A =[{:(-3,x),(4,2//3):}] does not have an inverse. Find the...

    Text Solution

    |

  17. There is a linear relationship between the number of chirps made by a ...

    Text Solution

    |

  18. If the length of the daimeter of a circle is equal to the length of th...

    Text Solution

    |

  19. The force of the wind on a sail varies jointly as the area of the sail...

    Text Solution

    |

  20. If the riser of each step in the drawing above is 6 inches and the tre...

    Text Solution

    |