Practice Problems on Zeros of Polynomials
Last updated at Oct. 6, 2020 by Teachoo
Last updated at Oct. 6, 2020 by Teachoo
Transcript
If ๐(๐ฅ) = ๐ฅ^2โ2โ2 ๐ฅ+1, then ๐(2 โ2) is equal to (a) 0 (b) 1 (c) 4โ2 (d) 8โ2 + 1Given ๐(๐ฅ)" = " ๐ฅ^2โ2โ2 ๐ฅ+1 Putting ๐=๐โ๐ ๐(2 โ2) = (2 โ2)^2โ(2โ2)(2โ2)+1 = 8 โ 8 + 1 = 1 Find p(0), p(1) and p(โ2) for the following polynomials (i) p(x) = 10x โ 4x2 โ 3 (ii) p(y) = (y + 2)(y โ 2)For p(x) = 10x โ 4x2 โ 3 p(0) = โ3 p(1) = 3 p(โ2) = โ39 For p(y) = (y + 2) (y โ 2) p(0) = โ4 p(1) = โ3 p(โ2) = 0 Zero of a Zero Polynomial is (a) 0 (b) 1 (c) Any real number (d) Not DefinedOne of the zeros of polynomial 2x2 โ 7x โ 4 is (a) 2 (b) 1/2 (c) (โ1)/2 (d) โ2Show that x = 1 is a root of polynomial 2x3 โ 3x2 + 7x โ 6 Let p(x) = 2x3 โ 3x2 + 7x โ 6 For x = 1 p(1) = 2(1)3 โ 3(1)2 + 7(1) โ 6 = 2 โ 3 + 7 โ 6 = 0 Since p(1) = 0 โด x = 1 is a root of p(x) Find zeros of polynomial in each of the following (i) p(x) = x โ 4 (ii) g(x) = 3 โ 6x (iii) q(x) = 2x โ 7 (iv) h(y) = 2yVerify whether true or false (i) โ3 is a zero of x โ 3 (ii) (โ1)/3 is a zero of 3x + 1 (iii) (โ4)/5 is a zero of 4 โ 5y (iv) 0 and 2 are zeros of t2 โ 2t (v) โ3 is a zero of y2 + y โ 6
Finding Zeroes of a polynomial
Finding Zeroes of a polynomial
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