Find the value of k for which x = 3 is a solution of the quadratic equation (k + 2)x² - kx + 6 = 0.
Thus, find the other root of the equation.

Question

Find the value of k for which x = 3 is a solution of the quadratic equation (k + 2)x^2 - kx + 6 = 0. Thus, find the other root of the equation.

KnowledgeBoat · Accepted Answer

Substituting, x = 3 in (k + 2)x2 - kx + 6 = 0 we get, ⇒ (k + 2)(3)2 - 3k + 6 = 0 ⇒ (k + 2)(9) - 3k + 6 = 0 ⇒ 9k + 18 - 3k + 6 = 0 ⇒ 6k + 24 = 0 ⇒ 6k = -24 ⇒ k = ⇒ k = -4. Substitute the value of k = -4 in (k + 2)x2 - kx + 6 = 0 we get, ⇒ (-4 + 2)(x)2 - (-4)x + 6 = 0 ⇒ (-2)(x)2 - (-4)x + 6 = 0 ⇒ -2x2 + 4x + 6 = 0 ⇒ -2x2 - 2x + 6x + 6 = 0 ⇒ -2x(x + 1) + 6(x + 1) = 0 ⇒ (x + 1)(-2x + 6) = 0 ⇒ (x + 1) = 0 or (-2x + 6) = 0 [Using Zero-product rule] ⇒ x = -1 or -2x = -6 ⇒ x = -1 or x = ⇒ x = -1 or x = 3. Hence, the value of k = -4 and the other root is -1.

Mathematics

Find the value of k for which x = 3 is a solution of the quadratic equation (k + 2)x² - kx + 6 = 0.
Thus, find the other root of the equation.

Quadratic Equations

Related Questions

Solve the following equation using quadratic formula:
x² - 4x + 1 = 0

Solve the following equation using quadratic formula:
9x² + 7x - 2 = 0

Mathematics

Find the value of k for which x = 3 is a solution of the quadratic equation (k + 2)x2 - kx + 6 = 0.Thus, find the other root of the equation.

Quadratic Equations

Related Questions

Solve the following equation using quadratic formula:x2 - 4x + 1 = 0

Solve the following equation using quadratic formula:9x2 + 7x - 2 = 0

Find the value of k for which x = 3 is a solution of the quadratic equation (k + 2)x² - kx + 6 = 0.
Thus, find the other root of the equation.

Solve the following equation using quadratic formula:
x² - 4x + 1 = 0

Solve the following equation using quadratic formula:
9x² + 7x - 2 = 0