if the equations x2-3x-k=0 and 4x2-11x+2k=0have a common root then find the value of k.also find theb common root?

Question

vikas askiitian expert · Answer

let c is the common root then c will stisfy both of these equations .

x²-3x-k = 0 .............1

4x²-11x+2k = 0 ............2

at x = c ,eq 1 becomes

c²-3c-k = 0

2c² - 6c - 2k = 0 ..............3 (after multiplying by 2)

at x = c, eq 2 becomes

4c²-11c+2k = 0 ................4

adding 3 & 4

6c² -17c = 0

c = 0 , 17/6

now , put c in any eq 3 or 4

then , k = 0,-17/36

(c,k) = { (0,0) ,(17/6,-17/36) }

this is the required solution ...

approve if u like my ans

Vikas TU · Answer

Take both as equations x 2 -3x-k = 0 .............1 4x 2 -11x+2k = 0 ............2 Solve it by eliminating method: 2x 2 -6x-2k = 0 [multiply by 2}........(3) now from eq. (2) and (3) 4x 2 -11x+2k = 0 2x 2 -6x-2k = 0 Solving these equations by eliminating method u will get: 6x 2 -17x = 0 .....................(4) x(6x-17) = 0 6x = 17 x = 0, 17/6 Put the value of x in eq...........(4) k = 0,-17/36 then, (c,k) = { (0,0) ,(17/6,-17/36) }

Vishruti · Answer

x 2 -4x+k = 0 and x 2 +kx-4 =0 have a common root, so let’s take it y putting value of y y 2 -4y+k=0 ----{1} y 2 -ky+4=0 ------{2} substracting {1} from {2} y 2 -4y+k-[ y 2 -ky+4] y 2 -4y+k-y 2 +ky-4=0 -y(k+4)+4+k=0 4+k= y(k+4) y=1 putting y=1 in eq {1} y 2 -4y+k=0 (1) 2 -4(1)+k=0 1-4+k=0 k=3

Thank you for registering.

Register Now and Win Upto 25% Scholorship for a Full Academic Year !

Enter Your Details

Registration done!

if the equations x2-3x-k=0 and 4x2-11x+2k=0have a common root then find the value of k.also find theb common root?

if the equations x2-3x-k=0 and 4x2-11x+2k=0have a common root then find the value of k.also find theb common root?

3 Answers

Think You Can Provide A Better Answer ?

Provide a better Answer & Earn Cool Goodies See our forum point policy

Other Related Questions on Algebra

ASK QUESTION

Answer and earn gift vouchers

View courses by askIITians

Design classes One-on-One in your own way with Top IITians/Medical Professionals

Complete Self Study Package designed by Industry Leading Experts

Live 1-1 coding classes to unleash the Creator in your Child

a Complete All-in-One Study package Fully Loaded inside a Tablet!

Register Now & Win Upto 25% Scholorship