Please help me with these questions. I am having trouble understanding what to do Please show all your work Thank you 2. For this question, you will prove that the roots of z² +6r+8.5 are irrational. In other words, thatVr € R, z² + 6 + 8.5=0=zQ.You may use, without proof, the quadratic formula. In other words, you may use the fact that for allreal a, b, and c,-b- -4ac4ac > 0) ⇒ (x=-b+√b² - 4ac2aVr € R, (ar²+bx+c=0) ^ (6²-4ac:) V (z =2aPlease write complete proofs in each subquestion, without referring back to earlier subquestions.1(a)Prove that Vr € R, z € Q⇒ (z+1) € Q. Hint: go back to the definition of Q, and showthat if a satisfies that definition, then so does (2+1).(b)Prove that Vr € R, z Q➡ (z+1) Q. Hint: can you prove the contrapositive of thisstatement?(c)Prove that VI ER,z² +6z+8.5=0⇒zQ. Hint: you may want to use results thatare similar to 2a and 26.

We need to prove that roots of are irrational.

For this question, you will prove that the roots of z² +6z+8.5 are irrational. In other words, that Vz € R, z² +6+8.5=0->zgQ. You may use, without proof, the quadratic formula. In other words, you may use the fact that for all real a, b, and c, -b-√²-4ac -b+√²-4ac 2a 2a Vz € R₁ (az²+bx+c=0) ^ (6² - 4ac ≥ 0) (z= 5) V (z Please write complete proofs in each subquestion, without referring back to earlier subquestions. (a) Prove that Vr € R, z € Q (z+1) € Q. Hint: go back to the definition of Q, and shou that if z satisfies that definition, then so does (z + 1). (b) Prove that Vr € R,r Q (z+1) g Q. Hint: can you prove the contrapositive of this statement? (c) Prove that Vz € R, z² +6z+8.5=0 zgQ. Hint: you may want to use results that are similar to 20 and 26.