Question

If x² - hx- 21=0, x² - 3hx+35=0 have a common root then h=?​

Answer 1

Answer:

• Let be the common roots of:  

  ² – ℎ – 21 = 0  

and  

  ² – 3ℎ + 35 = 0  

Then by definition of a root, we have the system:  

  {  ² – ℎ – 21 = 0  

  {  ² – 3ℎ + 35 = 0  

•  by Subtracting second equation from the first one we get :  

  (² – ℎ – 21) – (² – 3ℎ + 35) = 0 – 0  

  ² – ℎ – 21 – ² + 3ℎ – 35 = 0  

  ² – ² – ℎ + 3ℎ – 21 – 35 = 0  

  0 + 2ℎ – 56 = 0  

  2ℎ = 56  

  = 28/ℎ  

• Inserting this in the first equation:  

  ² – ℎ – 21 = 0  

  (28/ℎ)² – ℎ(28/ℎ) – 21 = 0      Since =28/ℎ  

  784/ℎ² – 28 – 21 = 0  

  784/ℎ² – 49 = 0  

  784/ℎ² = 49  

  16/ℎ² = 1                              Divide both sides by 49  

   16 = ℎ²                               Multiply both sides by ℎ²  

   ℎ = ±4  

• Now since we are told that ℎ>0, the solution ℎ=-4 is discarded leading to the final conclusion that:  

so ,   ℎ = 4      

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Answer 2

Answer:

4

Step-by-step explanation:

let a be the common root of:

x^2-hx-21=0

and

x^2-3hx+35=0

{a^2-ha-21=0

{a^2-3ha+35=0

subtracting secound equation from the first:

(a^2-ha-21)-(a^2-3ha-35)=0-0

a^2-ha-21-a^2+3ha-35=0

a^2-a^2-ha+3ha-21-35=0

0+2ha-56=0

2ha=56

a=56/2h

a=28/h

Inserting this in the first EQUATION :

a^2-ha-21=0 since a= 28/h

(28/h)^2-h(28/h)-21=0

784/h^2-28-21=0

784/h^2-49=0

784/h^2=49

16/h^2=1

16=h^2

h= root 16

h=4

I hope this answer will help you