Verify whether the following are zeroes of the polynomial, indicated against them. (i) p(x) = 3x + 1, x = -1/3(ii) p(x) = 5x - π, x = -4/5(iii) p(x) = x² - 1, x = 1, -1 (iv) p(x) = (x + 1)(x - 2), x = -1, 2 (v) p(x) = x², x = 0 (vi) p(x) = lx + m, x = -m/l(vii) p(x) = 3x² - 1, x = -1/√3 ,2√3 (viii) p(x) = 2x + 1, x = 1/2

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KnowledgeBoat · Accepted Answer

(i) p(x) = 3x + 1 Putting x = we get, = + 1 = -1 + 1 = 0 Hence, x = is zeroes of this polynomial. (ii) p(x) = 5x - π Putting x = we get, = 4 - π Hence, x = is not a zeroes of this polynomial. (iii) p(x) = x² - 1 Putting x = 1 we get, p(1) = (1)² - 1 = 0 Putting x = -1 we get p(-1) = (-1)² - 1 = 1 - 1 = 0 Hence, x = 1, -1 is zeroes of this polynomial. (iv) p(x) = (x + 1)(x - 2) Putting x = -1 we get, p(1) = (-1 + 1)(-1 - 2) = 0 x (-3) = 0 Putting x = 2 we get, p(2) = (2 + 1)(2 - 2) = 3 x 0 = 0 Hence, x = -1, 2 are the zeroes of this polynomial. (v) p(x) = x² Putting x = 0 we get, p(0) = (0)² = 0 Hence, x = 0 is the zero of this polynomial. (vi) p(x) = lx + m Putting x = - we get, p - + m = -m + m = 0 Hence, x = is the zero of this polynomial. (vii) p(x) = 3x² - 1 Putting x = we get, p- = 3 x -² - 1 = 3 x - 1 = 1 - 1 = 0 Putting x = we get, p = 3 x ² - 1 = 3 x - 1 = 4 - 1 = 3 Hence, x = is zeroes of polynomial but x = is not a zeroes of this polynomial. (viii) p(x) = 2x + 1 Putting x = we get, p = 2 x + 1 = 1 + 1 = 2 No, x = is not the zeroes of this polynomial.

Mathematics

Polynomials

Related Questions

Find the value of the polynomial 5x - 4x² + 3 at
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(ii) x = -1
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Find p(0), p(1) and p(2) for each of the following polynomials:
(i) p(y) = y² - y + 1
(ii) p(t) = 2 + t + 2t² - t³
(iii) p(x) = x³
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Find the zero of the polynomial in each of the following cases:
(i) p(x) = x + 5
(ii) p(x) = x - 5
(iii) p(x) = 2x + 5
(iv) p(x) = 3x - 2
(v) p(x) = 3x
(vi) p(x) = ax, a ≠ 0
(vii) p(x) = cx + d, c ≠ 0, c, d are real numbers.

Mathematics

Polynomials

Related Questions

Find the value of the polynomial 5x - 4x2 + 3 at(i) x = 0(ii) x = -1(iii) x = 2

Find p(0), p(1) and p(2) for each of the following polynomials:(i) p(y) = y2 - y + 1(ii) p(t) = 2 + t + 2t2 - t3(iii) p(x) = x3(iv) p(x) = (x - 1) (x + 1)

Find the zero of the polynomial in each of the following cases:(i) p(x) = x + 5(ii) p(x) = x - 5(iii) p(x) = 2x + 5(iv) p(x) = 3x - 2(v) p(x) = 3x(vi) p(x) = ax, a ≠ 0(vii) p(x) = cx + d, c ≠ 0, c, d are real numbers.

Find the value of the polynomial 5x - 4x² + 3 at
(i) x = 0
(ii) x = -1
(iii) x = 2

Find p(0), p(1) and p(2) for each of the following polynomials:
(i) p(y) = y² - y + 1
(ii) p(t) = 2 + t + 2t² - t³
(iii) p(x) = x³
(iv) p(x) = (x - 1) (x + 1)

Find the zero of the polynomial in each of the following cases:
(i) p(x) = x + 5
(ii) p(x) = x - 5
(iii) p(x) = 2x + 5
(iv) p(x) = 3x - 2
(v) p(x) = 3x
(vi) p(x) = ax, a ≠ 0
(vii) p(x) = cx + d, c ≠ 0, c, d are real numbers.