RS Aggarwal - Mathematics

Book: RS Aggarwal - Mathematics

Chapter: 2. Polynomials

Subject: Maths - Class 10th

Q. No. 12 of Exercise 2B

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12

It is given that ‒1 is one of the zeros of the polynomial x3 + 2x2 ‒ 11x ‒ 12. Find all the zeros of the given polynomial.

Let us assume f (x) = x3 + 2x2 ‒ 11x ‒ 12

It is given in the question that, -1 is a zero of the polynomial


(x + 1) is a factor of f (x)


Now on dividing f (x) by (x + 1), we get



f (x) = x3 + 2x2 ‒ 11x ‒ 12


= (x + 1) (x2 + x – 12)


= (x + 1) {x2 + 4x – 3x – 12}


= (x + 1) {x (x + 4) – 3 (x + 4)}


= (x + 1) (x – 3) (x + 4)


f (x) = 0


(x + 1) (x – 3) (x + 4) = 0


(x + 1) = 0 0r (x – 3) = 0 or (x + 4) = 0


x = -1 or x = 3 or x = - 4


Hence, zeros of the polynomial are -1, 3 and -4


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