1 karansingh Asked: January 17, 20232023-01-17T11:52:45+05:30 2023-01-17T11:52:45+05:30In: CBSE If the remainder on division of x3 + 2×2 + kx +3 by x – 3 is 21, find the quotient and the value of k. Hence, find the zeroes of the cubic polynomial x3 + 2×2 + kx – 18. 1 This question is very tricky. its an important 5 mark question for boards exam cbseclass 10polynomials Share Facebook 1 Answer Voted Oldest Recent Areeb khalid 2023-01-20T10:50:23+05:30Added an answer on January 20, 2023 at 10:50 am Given, p(x) = x³ + 2x² + kx +3 g(x) = x – 3 Remainder, r(x=3) = 21. We have to find the quotient and the value of k and the zeros of the cubic polynomial. The division algorithm states that given any polynomial p(x) and any non-zero polynomial g(x), there are polynomials q(x) and r(x) such that p(x) = g(x) q(x) + r(x) To find the value of k, put x = 3 in p(x), p(3) = (3)³ + 2(3)² + k(3) +3 = 21 27 + 18 + 3k + 3 = 21 48 + 3k = 21 3k = -27 k = -27/3 k = -9 Therefore, the cubic polynomial is x³ + 2x² – 9x + 3. Using long division to find the quotient, The quotient is x² + 5x + 6. On factoring, x² + 5x + 6 = 0 x² +3x + 2x + 6 = 0 x(x + 3) + 2(x + 3) = 0 (x + 2)(x + 3) = 0 Now, x + 2 = 0 x = -2 Also, x + 3 = 0 x = -3 Therefore, the zeros of the polynomial are 3, -2 and -3 -1 Reply Share Share Share on Facebook Share on Twitter Share on LinkedIn Share on WhatsApp Leave an answerLeave an answerCancel reply Featured image Select file Browse Add a Video to describe the problem better. Video type Youtube Vimeo Dailymotion Facebook Choose from here the video type. Video ID Put Video ID here: https://www.youtube.com/watch?v=sdUUx5FdySs Ex: "sdUUx5FdySs". Click on image to update the captcha. Save my name, email, and website in this browser for the next time I comment. Related Questions Speed of a boat in still water is 15 km/h. It goes 30 km upstream and returns back ... Find the values of k for which the pair of linear equations kx + 3y = k-2 and ... . Solve for x and y: 0.4x-1.5y = 6.5, 0.3x-0.2y=0.9. Solve graphically the system of linear equations 4x-5y +16=0 and 2x+y-6 = 0. Determine the vertices of the ... Given that x – √5 is a factor of the polynomial x3 – 3√5x2 – 5x + 15√5, ...

Given, p(x) = x³ + 2x² + kx +3

g(x) = x – 3

Remainder, r(x=3) = 21.

We have to find the quotient and the value of k and the zeros of the cubic polynomial.

The division algorithm states that given any polynomial p(x) and any non-zero

polynomial g(x), there are polynomials q(x) and r(x) such that

p(x) = g(x) q(x) + r(x)

To find the value of k, put x = 3 in p(x),

p(3) = (3)³ + 2(3)² + k(3) +3 = 21

27 + 18 + 3k + 3 = 21

48 + 3k = 21

3k = -27

k = -27/3

k = -9

Therefore, the cubic polynomial is x³ + 2x² – 9x + 3.

Using long division to find the quotient,

The quotient is x² + 5x + 6.

On factoring,

x² + 5x + 6 = 0

x² +3x + 2x + 6 = 0

x(x + 3) + 2(x + 3) = 0

(x + 2)(x + 3) = 0

Now, x + 2 = 0

x = -2

Also, x + 3 = 0

x = -3

Therefore, the zeros of the polynomial are 3, -2 and -3