If one of the zeroes of the cubic polynomial x3 + px² + qx + r is -1, then the product of the other two zeroes is
(a) p + q + 1
(b) p-q- 1
(c) q – p + 1
(d) q – p – 1
please solve step by step...I will mark you as brainliest...I will give rating if the answer is correct with valid steps
Answers
Answer:
Are u sure the question is correct?
SOLUTION
TO CHOOSE THE CORRECT OPTION
If one of the zeroes of the cubic polynomial x³ + px² + qx + r is - 1 , then the product of the other two zeroes is
(a) p + q + 1
(b) p - q - 1
(c) q – p + 1
(d) q – p – 1
EVALUATION
Here the given cubic polynomial is
x³ + px² + qx + r
Since - 1 is one of the zeroes then
( - 1)³ + p × (-1)² + q × (-1) + r = 0
⇒ - 1 + p - q + r = 0
⇒ r = - p + q + 1
Let the three zeros of the cubic polynomial are α , β , γ
Such that γ = - 1
Then
α + β + γ = - p
αβ + βγ + γα = q
α β γ = - r
Now α β γ = - r gives
α β × ( - 1 ) = - r
⇒ α β = r
⇒ α β = - p + q + 1
⇒ α β = q - p + 1
FINAL ANSWER
Hence the correct option is (c) q – p + 1
━━━━━━━━━━━━━━━━
Learn more from Brainly :-
write a quadratic polynomial sum of whose zeroes is 2 and product is -8
https://brainly.in/question/25501039
2. The quadratic polynomial where α=5+2√6 and αβ=1 is
https://brainly.in/question/24697408