Tip:A–D to answerE for explanationV for videoS to reveal answer
Let a∈R and let α,β be the roots of the equation x2+6041x+a=0. If α4+β4=−30, then the product of all possible values of a is
- A.
45
(Correct Answer) - B.
46
- C.
47
- D.
48
Explanation
Solving:
-
α+β=−6041, αβ=a
-
α2+β2=(α+β)2−2αβ=(6041)2−2a=60−2a
-
α4+β4=(α2+β2)2−2(αβ)2
-
−30=(60−2a)2−2a2
-
−30=60+4a2−4a60−2a2
-
2a2−460a+90=0
-
a2−260a+45=0
-
Product of values of a: coefficient of a2constant term=145=45
Answer: 45
Explanation
Solving:
-
α+β=−6041, αβ=a
-
α2+β2=(α+β)2−2αβ=(6041)2−2a=60−2a
-
α4+β4=(α2+β2)2−2(αβ)2
-
−30=(60−2a)2−2a2
-
−30=60+4a2−4a60−2a2
-
2a2−460a+90=0
-
a2−260a+45=0
-
Product of values of a: coefficient of a2constant term=145=45
Answer: 45
