501.On dividing the polynomial 10x4 – 6x3 – 40x2 + 41x – 5 by the polynomial g(x), the quotient is 5x - 3 and remainder is 2x + 4. Find the polynomial g(x).
502.Find the zeroes of the quadratic polynomial f(x,) = abx2 + (b2 –ac) x– bc and verify the relationship between the zeroes and its coefficients.
Solution not provided. Ans.Â
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503.Divide the polynomial p(x) by the polynomial g(x) and find the quotient and reaminder in the following: p(x) = x2 + 5x + 7, g(x) = x + 2
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504.Find the values of p and q so that x4Â + x3Â + 8x2Â +px + q is divisible by x2Â + 1.
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505.What must be subtracted from 8x4 + 14x3–2x2 + 7x – 8 so that the resulting polynomial is exactly divisible by 4x2 + 3x – 2?
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506.
Find the quadratic polynomials, some of whose zeroes is 8 and their product is 12. Hence, find the zeroes at the polynomial.
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507.Write the no of zeroes of the polynomial y = f (x) whose graph is given in fig:
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Long Answer Type
508.Using division algorithm, find the quotient and remainder on dividing f(x) by f(x), where f(x) = 6x3 + 3x2 + x – 2 and g(x) = 2x + 1.
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Short Answer Type
509.Find all the zeroes x4– 3x3 + 6x–4, if two of its zeroes areÂ
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510.Find all zeroes of the polynomial x4 + x3 – 34x2– 4x + 120, if two of its zeroes are 2 and –2.
Short Answer Type
Long Answer Type
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