Question 1133934: Given that p is a root of equations x^2-x-q=0 and -x^2-7x+q+8=0, find the values of p and q
Answer by algebrahouse.com(1659)   (Show Source):
You can put this solution on YOUR website! x² - x - q = 0
-x² - 7x + q = -8 ← subtracted 8 from both sides of second equation
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-8x = -8 ← added the two equations
x = 1
Since p "is a root", then p = 1
If x = 1:
(1)² - 1 - q = 0 ← substituted 1 into first equation
1 - 1 - q = 0 ← evaluated exponent
-q = 0 ← subtracted
q = 0 ← divided each side by -1
Check by putting 1 back in for x and 0 in for q into first equation
(1)² - 1 - 0 = 0 ← substituted 1 for x and 0 for q into 1st equation
1 - 1 - 0 = 0 ← evaluated exponent
0 = 0 checks
Check by putting 1 back in for x and 0 in for q into second equation
-(1)² - 7(1) + 0 + 8 = 0 ← substituted 1 for x and 0 for q into 2nd equation
-1 - 7 + 0 + 8 = 0 ← evaluated exponent
0 = 0 checks
p = 1 and q = 0
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