MathematicsFind the value of μ for which one root of the quadratic equation μx2−14x+8 = 0 is 6 times the other.

Find the value of μ for which one root of the quadratic equation μx2−14x+8 = 0 is 6 times the other.


  1. A
    5
  2. B
    4
  3. C
    3
  4. D
    2 

    Fill Out the Form for Expert Academic Guidance!l



    +91



    Live ClassesBooksTest SeriesSelf Learning



    Verify OTP Code (required)

    I agree to the terms and conditions and privacy policy.

    Solution:

    Given: The quadratic equation is μx2−14x+8 = 0
    One root of the equation given is 6 times the other.
    We need to find the value of μ
    Let the roots of the given quadratic equation be α and β respectively.
    According to the question,
     α is 6 times of β
     ⇒α=6×β
    Sum of the roots of the equation in general form ax2+bx+c=0 is -ba
    Comparing the given equation μx2−14x+8 = 0 with the general form, we get
     a=μ
    b=−14
    c=8
     α+β=-ba  = -(-14μ)
     α+β=14μ ..Equation (1)
    Given that α=6×β
    Substituting α=6×β in Equation (1)
    We get,
     6β+β=14μ
    7β=14μ
     β=2μ ..Equation (2)
    Product of the roots of the equation in general form ax2+bx+c=0 is ca
     α×β=ca=8μ ..Equation (3)
    Substituting α=6×β in Equation (3)
    We get,
     6β×β=8μ
     6β2=8μ ..Equation (4)
    Substituting Equation (2) in Equation (4) , we get
     6×2μ2=8μ
    6×4μ2=8μ
    μ=3
    Therefore, the value of μ is 3.
     
    Chat on WhatsApp Call Infinity Learn

      Talk to our academic expert!



      +91


      Live ClassesBooksTest SeriesSelf Learning




      Verify OTP Code (required)

      I agree to the terms and conditions and privacy policy.