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