Question

32. On dividing p(x) = x - 3x + x + 2 by a polynuna que
respectively. Find g(x).
33.If the sum of the zeroes of the polynomial p(x) = (k2 – 14) x2 – 2x – 12 is 1, then find the value of k.
34.If a and B are the zeroes of a polynomial such that a + B = -6 and aß = 5, then find the polynomial.
35. Form a quadratic polynomial whose zeroes are 3 + V2 and 3 – V2.
36. Find a quadratic polynomial, the sum and product of whose zeroes are v3 and 1/13 respectively.
Questions from 37 to 39 carries 3 marks each
37. Find the zeroes of the quadratic polynomial v3 x? – 8x + 4v3.
38. Find the zeroes of p(x) = 2x? – X-6 and verify the relationship of zeroes with these co-efficients.
39. Find a quadratic polynomial, the sum and product of whose zeroes are -8 and 12 respectively.
Hence find the zeroes.​

Answer 1

Answer:

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Step-by-step explanation:

We know that the division algorithm states that:

Dividend=(Divisor×quotient)+Remainder

Here it is given that the dividend is p(x)=4x

3

+2x

2

−10x+2, the divisor is g(x), the quotient is 2x

2

+4x+1 and the remainder is 5, therefore,

4x

3

+2x

2

−10x+2=[g(x)(2x

2

+4x+1)]+5

⇒g(x)=

2x

2

+4x+1

4x

3

+2x

2

−10x+2

The division is shown above.

Hence, from the above division, we get that the divisor is g(x)=2x−3