Request a call back

Join NOW to get access to exclusive study material for best results

CBSE Class 10 Answered

question
Asked by arindeep.singh | 26 Sep, 2020, 10:39: AM
Expert Answer
Q: Does there exist a quadratic equation whose coefficients are all distinct irrationals but both the roots are rationals? Why?
Solution:
Yes, it is possible that a quadratic equation with distinct irrational coefficients have rational roots.
It is because, the roots are rational if the discriminant is a perfect square. So, it depends upon the discriminant and not on the coefficients.
 
Here is an example:
square root of 3 straight x squared minus square root of 27 straight x plus square root of 12 equals 0
straight x equals fraction numerator negative straight b plus-or-minus square root of straight b squared minus 4 ac end root over denominator 2 straight a end fraction
equals fraction numerator square root of 27 plus-or-minus square root of 27 minus 4 open parentheses square root of 3 close parentheses open parentheses square root of 12 close parentheses end root over denominator 2 square root of 3 end fraction
equals fraction numerator 3 square root of 3 plus-or-minus square root of 27 minus 24 end root over denominator 2 square root of 3 end fraction
equals fraction numerator square root of 3 open parentheses 3 plus-or-minus 1 close parentheses over denominator 2 square root of 3 end fraction
equals fraction numerator 3 plus-or-minus 1 over denominator 2 end fraction
equals 2 space or space 1
Answered by Renu Varma | 28 Sep, 2020, 11:00: AM
CBSE 10 - Maths
Asked by atharvsharma971 | 06 Jun, 2022, 10:30: PM
ANSWERED BY EXPERT
CBSE 10 - Maths
Asked by zk4656260 | 31 May, 2022, 05:32: PM
ANSWERED BY EXPERT
CBSE 10 - Maths
Asked by ankur.spsharma | 02 May, 2022, 11:54: AM
ANSWERED BY EXPERT
CBSE 10 - Maths
Asked by nehakoushik101 | 01 May, 2022, 09:13: PM
ANSWERED BY EXPERT
CBSE 10 - Maths
Asked by iambkhatun343 | 14 Feb, 2022, 12:57: AM
ANSWERED BY EXPERT
CBSE 10 - Maths
Asked by semilmasani6005 | 28 Dec, 2020, 01:45: PM
ANSWERED BY EXPERT
CBSE 10 - Maths
Asked by jaishpal15chouhan | 25 Oct, 2020, 07:33: PM
ANSWERED BY EXPERT
CBSE 10 - Maths
Asked by arindeep.singh | 26 Sep, 2020, 10:41: AM
ANSWERED BY EXPERT
CBSE 10 - Maths
Asked by arindeep.singh | 26 Sep, 2020, 10:39: AM
ANSWERED BY EXPERT
CBSE 10 - Maths
Asked by arindeep.singh | 26 Sep, 2020, 10:35: AM
ANSWERED BY EXPERT

Start your hassle free Education Franchisee and grow your business!

Know more
×