Max' brother is M-6 years old.
2,3,7,and 5 are the factors
Step-by-step explanation:
A. x^2-9x+18
B. x^2-8x+16
C. 2x^2-5x-12
D. 12x^2-31x+7
The valid exclusion of the algebraic fraction is (c) a =0, b =0, a =2b
<h3>How to determine the valid exclusion?</h3>
The expression is given as:
8ab^2x/4a^2b - 8ab^2
Set the denominator to 0
4a^2b - 8ab^2 = 0
Divide through by 4ab
a - 2b = 0
Add 2b to both sides
a = 2b
Hence, the valid exclusion of the algebraic fraction is (c) a =0, b =0, a =2b
Read more about algebraic fraction at:
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You did it right (almost, I got 21 instead of 19) but didn't finish. You need to show your discriminant is never negative.
x² + (p+1)x = 5-2p
x² + (p+1)x +(2p-5) =0
Real roots mean a positive (or at least non-negative) discriminant:
D = b² - 4ac = (p+1)² - 4(1)(2p - 5) = p² + 2p + 1 - 8p + 20
D = p² - 6p + 21
It's not totally obvious that D>0; we prove that by completing the square by noting
(p-3)² = p² - 6p + 9
so
p² - 6p = (p-3)² - 9.
D = p² - 6p + 21
D = (p-3)² - 9 + 21
D = (p-3)² + 12
Now we clearly see D>0 always because the squared term can't be negative, so D is always at least 12. We always get two distinct real roots.
