Math, asked by jeevitadhri, 8 months ago

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

Answered by charusatija0702
8

Answer:

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Answered by pulakmath007
8

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

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