If x^2 - hx - 21 = 0, x^2 - hx + 35 = 0 have a common root then h is 1) +- 2 2) +- 4 3) +- 6 4) +- 8
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
► Subtracting second equation from the first yields:
(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:
ℎ = 4 ◄ANSWER
Step-by-step explanation:
please mark me as brainlist
Answer:
Now since we are told that ℎ>0, the solution ℎ=-4 is discarded leading to the final conclusion that:
ℎ = 4
Step-by-step explanation:
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
► Subtracting second equation from the first yields:
(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