Answer:
4x + 2
Step-by-step explanation:
x - 1 is adding an x and subtracting a 1 ,so
x + x + x + (x - 1) + 1 + 1 + 1
= x + x + x + x - 1 + 1 + 1 + 1 ← collect like terms
= 4x + 2
There are two sides in a coin so the chance of getting tails is 1/2, which would be 0.5.
I'm not sure tho.
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.
