Question

plzzz answer all and i will give 50 points on next question​

Answer 1

Q 2) x2-5x+k

Here, a=1, b=-5 and c=k

Now, α+ β = -b/a= -(-5)/1= 5

α*β = c/a= k/7= k

Now,α - β =1

Squaring both sides, we get,

(α - β)2=12

⇒ α2 + β2 - 2αβ = 1

⇒ (α2 + β2 + 2αβ) - 4αβ = 1

⇒ (α +β)2 -4αβ =1

⇒ (5)2-4k=1

⇒ -4k= 7-25

⇒ -4k= -24

⇒ k=6 So the value of k is 6.

Answer 2

(1) Let us assume on the contrary that 5−√3 is rational. Then, there exist prime positive integers a

and b such that

5-√3=a/b

⇒5-a/b=√3

⇒√3 is rational

[∵a,b are integers∴ (5b−a)/b is a rational number]

This contradicts the fact that √3 is irrational.

So, our assumption is incorrect. Hence, 5−√3 is an irrational number.

(6) Basic Proportionality Theorem states that "If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, the other two sides are divided in the same ratio".

Thales Theorem Statement states that "If a line is drawn parallel to one side of a triangle intersecting the other two sides in distinct points, then the other two sides are divided in the same ratio".