Solve : (a + b)²x² - (a + b)x - 6 = 0; a + b ≠ 0.

Question

KnowledgeBoat · Accepted Answer

Let (a + b)x = y ⇒ (a + b)²x² - (a + b)x - 6 = 0 ⇒ y² - y - 6 = 0 ⇒ y² - 3y + 2y - 6 = 0 ⇒ y(y - 3) + 2(y - 3) = 0 ⇒ (y + 2)(y - 3) = 0 ⇒ (y + 2) = 0 or y - 3 = 0 ⇒ y = -2 or y = 3. ∴ (a + b)x = -2 or (a + b)x = 3 ⇒ x = . Hence, x =

Mathematics

Solve :
(a + b)²x² - (a + b)x - 6 = 0; a + b ≠ 0.

Quadratic Equations

Related Questions

Show that one root of the quadratic equation x² + (3 - 2a)x - 6a = 0 is -3. Hence, find its other root.

Find the solution of the quadratic equation 2x² - mx - 25n = 0; if m + 5 = 0 and n - 1 = 0.

Without solving the following quadratic equation, find the value of 'm' for which the given equation has real and equal roots.
x² + 2(m - 1)x + (m + 5) = 0

Find the value of k for which equation 4x² + 8x - k = 0 has real roots.

Mathematics

Solve :(a + b)2x2 - (a + b)x - 6 = 0; a + b ≠ 0.

Quadratic Equations

Related Questions

Show that one root of the quadratic equation x2 + (3 - 2a)x - 6a = 0 is -3. Hence, find its other root.

Find the solution of the quadratic equation 2x2 - mx - 25n = 0; if m + 5 = 0 and n - 1 = 0.

Without solving the following quadratic equation, find the value of 'm' for which the given equation has real and equal roots.x2 + 2(m - 1)x + (m + 5) = 0

Find the value of k for which equation 4x2 + 8x - k = 0 has real roots.

Solve :
(a + b)²x² - (a + b)x - 6 = 0; a + b ≠ 0.

Show that one root of the quadratic equation x² + (3 - 2a)x - 6a = 0 is -3. Hence, find its other root.

Find the solution of the quadratic equation 2x² - mx - 25n = 0; if m + 5 = 0 and n - 1 = 0.

Without solving the following quadratic equation, find the value of 'm' for which the given equation has real and equal roots.
x² + 2(m - 1)x + (m + 5) = 0

Find the value of k for which equation 4x² + 8x - k = 0 has real roots.