badge image

Enroll For Free Now & Improve Your Performance.

×
User Icon
User Icon
User Icon
User Icon
User Icon

Thank you for registering.

One of our academic counsellors will contact you within 1 working day.

Please check your email for login details.
MY CART (5)

Use Coupon: CART20 and get 20% off on all online Study Material

ITEM
DETAILS
MRP
DISCOUNT
FINAL PRICE
Total Price: Rs.

There are no items in this cart.
Continue Shopping
Menu
Grade: 10

                        

1. given that the zeroes of the cubic polynimial x 3 - 6x 2 +3x+10 are of the form a, a+b, a+2b for some real no.s a and b. find the values of a and b as well as the zeroes of the given polynomial

1. given that the zeroes of the cubic polynimial   x- 6x2+3x+10 are of the form a, a+b, a+2b for some real no.s a and b. find the values of a and b as well as the zeroes of the given polynomial

    3 years ago

    Answers : (1)

    Arun
    25768 Points
    							
    Dear student
     
    Given that a, a+b, a+2b are roots of given polynomial x³-6x²+3x+10

    From this polynomial,
    Sum of the roots 
    ⇒ a+2b+a+a+b = -coefficient of x²/ coefficient of x³
                               ⇒ 3a+3b = -(-6)/1 = 6
                               ⇒ 3(a+b) = 6
                               ⇒ a+b = 2  --------- (1)  b = 2-a

    Product of roots ⇒ (a+2b)(a+b)a = -constant/coefficient of x³
                              ⇒ (a+b+b)(a+b)a = -10/1

    Placing the value of a+b=2 in it
                             ⇒ (2+b)(2)a = -10
                             ⇒ (2+b)2a = -10
                             ⇒ (2+2-a)2a = -10
                             ⇒ (4-a)2a = -10
                             ⇒ 4a-a² = -5
                             ⇒ a²-4a-5 = 0
                             ⇒ a²-5a+a-5 = 0
                             ⇒ (a-5)(a+1) = 0
                          a-5 = 0      or        a+1 = 0
                          a = 5                     a = -1                

      a = 5, -1 in (1) a+b = 2

    When a = 5, 5+b=2 ⇒ b=-3
               a = -1, -1+b=2 ⇒ b= 3

    ∴ If a=5 then b= -3
                or
       If a= -1 then b=3
     
    Regards
    Arun (askIITians forum expert)
    3 years ago
    Think You Can Provide A Better Answer ?
    Answer & Earn Cool Goodies


    Course Features

    • 728 Video Lectures
    • Revision Notes
    • Previous Year Papers
    • Mind Map
    • Study Planner
    • NCERT Solutions
    • Discussion Forum
    • Test paper with Video Solution


    Course Features

    • 731 Video Lectures
    • Revision Notes
    • Test paper with Video Solution
    • Mind Map
    • Study Planner
    • NCERT Solutions
    • Discussion Forum
    • Previous Year Exam Questions


    Ask Experts

    Have any Question? Ask Experts

    Post Question

     
     
    Answer ‘n’ Earn
    Attractive Gift
    Vouchers
    To Win!!! Click Here for details