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Grade: 11
        
If x2-hx-21=0,x2-3hx+35=0(h>0)has a common root ,then value of h is equal to 
A 1.  B  2.   C 3. D 4.
one year ago

Answers : (1)

Arun
23036 Points
							
► Let 𝑎 be the common roots of: 
   𝑥² – ℎ𝑥 – 21 = 0 
and 
   𝑥² – 3ℎ𝑥 + 35 = 0 

Then by definition of a root, we have the system: 
   {  𝑎² – ℎ𝑎 – 21 = 0 
   {  𝑎² – 3ℎ𝑎 + 35 = 0 

► Subtracting second equation from the first yields: 
   (𝑎² – ℎ𝑎 – 21) – (𝑎² – 3ℎ𝑎 + 35) = 0 – 0 
   𝑎² – ℎ𝑎 – 21 – 𝑎² + 3ℎ𝑎 – 35 = 0 
   𝑎² – 𝑎² – ℎ𝑎 + 3ℎ𝑎 – 21 – 35 = 0 
   0 + 2ℎ𝑎 – 56 = 0 
   2ℎ𝑎 = 56 
   𝑎 = 28/ℎ 

► Inserting this in the first equation: 
   𝑎² – ℎ𝑎 – 21 = 0 
   (28/ℎ)² – ℎ(28/ℎ) – 21 = 0    ← Since 𝑎=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: 
   ℎ = 4        ◄ANSWER
one year ago
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