Find the value of k, if x - 1 is a factor of p(x) in each of the following cases: (i) p(x) = x^2 + x + k (ii) p(x) = 2x^2 + kx + (iii) p(x) = kx^2 - x + 1 (iv) p(x) = kx^2 - 3x + k

Question

Find the value of k, if x - 1 is a factor of p(x) in each of the following cases: (i) p(x) = x^2 + x + k (ii) p(x) = 2x^2 + kx + (iii) p(x) = kx^2  - x + 1 (iv) p(x) = kx^2  - 3x + k

KnowledgeBoat · Accepted Answer

(i) p(x) = x² + x + k ⇒ x - 1 = 0 ⇒ x = 1 Putting x = 1 we get, p(1) = (1)² + 1 + k = 1 + 1 + k ⇒ 2 + k = 0 ⇒ k = -2 So the value of k = -2 (ii) p(x) = 2x² + kx + ⇒ x - 1 = 0 ⇒ x = 1 Putting x = 1 we get, p(1) = 2(1)² + k(1) + ⇒ 2 + k + ⇒ k = -2 - ⇒ k = -(2 + ) So the value of k = -(2 + ) (iii) p(x) = kx² - x + 1 ⇒ x - 1 = 0 ⇒ x = 1 Putting x = 1 we get, p(1) = k(1)² - (1) + 1 ⇒ k - + 1 = 0 ⇒ k = - 1 So the value of k = - 1 (iv) p(x) = kx² - 3x + k ⇒ x - 1 = 0 ⇒ x = 1 Putting x = 1 we get, p(1) = k(1)² -3(1) + k = k - 3 + k ⇒ 2k - 3 = 0 ⇒ 2k = 3 ⇒ k = So the value of k =

Mathematics

Find the value of k, if x - 1 is a factor of p(x) in each of the following cases: (i) p(x) = x^2 + x + k (ii) p(x) = 2x^2 + kx + (iii) p(x) = kx^2 - x + 1 (iv) p(x) = kx^2 - 3x + k

Polynomials

Related Questions

Use the Factor Theorem to determine whether g(x) is a factor of p(x) in each of the following cases:
(i) p(x) = 2x³ + x² - 2x - 1, g(x) = x + 1
(ii) p(x) = x³ + 3x² + 3x + 1, g(x) = x + 2
(iii) p(x) = x³ - 4x² + x + 6, g(x) = x - 3

Factorise :
(i) 12x² - 7x + 1
(ii) 2x² + 7x + 3
(iii) 6x² + 5x - 6
(iv) 3x² - x - 4

Factorise :
(i) x³ - 2x² - x + 2
(ii) x³ - 3x² - 9x - 5
(iii) x³ + 13x² + 32x + 20
(iv) 2y³ + y² - 2y - 1

Mathematics

Find the value of k, if x - 1 is a factor of p(x) in each of the following cases: (i) p(x) = x^2 + x + k (ii) p(x) = 2x^2 + kx + (iii) p(x) = kx^2 - x + 1 (iv) p(x) = kx^2 - 3x + k

Polynomials

Related Questions

Use the Factor Theorem to determine whether g(x) is a factor of p(x) in each of the following cases:(i) p(x) = 2x3 + x2 - 2x - 1, g(x) = x + 1(ii) p(x) = x3 + 3x2 + 3x + 1, g(x) = x + 2(iii) p(x) = x3 - 4x2 + x + 6, g(x) = x - 3

Factorise :(i) 12x2 - 7x + 1(ii) 2x2 + 7x + 3(iii) 6x2 + 5x - 6(iv) 3x2 - x - 4

Factorise :(i) x3 - 2x2 - x + 2(ii) x3 - 3x2 - 9x - 5(iii) x3 + 13x2 + 32x + 20(iv) 2y3 + y2 - 2y - 1

Use the Factor Theorem to determine whether g(x) is a factor of p(x) in each of the following cases:
(i) p(x) = 2x³ + x² - 2x - 1, g(x) = x + 1
(ii) p(x) = x³ + 3x² + 3x + 1, g(x) = x + 2
(iii) p(x) = x³ - 4x² + x + 6, g(x) = x - 3

Factorise :
(i) 12x² - 7x + 1
(ii) 2x² + 7x + 3
(iii) 6x² + 5x - 6
(iv) 3x² - x - 4

Factorise :
(i) x³ - 2x² - x + 2
(ii) x³ - 3x² - 9x - 5
(iii) x³ + 13x² + 32x + 20
(iv) 2y³ + y² - 2y - 1