Solve : (x/x + 2)^2 - 7(x/x + 2) + 12 = 0; x ≠ -2.

Substituting = a in above equation we get, ⇒ a 2 - 7a + 12 = 0 ⇒ a 2 - 4a - 3a + 12 = 0 ⇒ a(a - 4) - 3(a - 4) = 0 ⇒ (a - 3)(a - 4) = 0 ⇒ (a - 3) = 0 or (a - 4) = 0 ⇒ a = 3 or a = 4. Considering, ⇒ x = 3(x + 2) ⇒ x = 3x + 6 ⇒ 3x - x = -6 ⇒ 2x = -6 ⇒ x = -3. Considering, ⇒ x = 4(x + 2) ⇒ x = 4x + 8 ⇒ 4x - x = -8 ⇒ 3x = -8 ⇒ x = -. Hence, x = -3, -.

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

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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

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

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If -2 is a root of the equation 3x² + 7x + p = 1, find the value of p. Now find the value of k so that the roots of the equation x² + k(4x + k - 1) + p = 0 are equal.

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Mathematics

Solve : (x/x + 2)^2 - 7(x/x + 2) + 12 = 0; x ≠ -2.

Quadratic Equations

Related Questions

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

If -2 is a root of the equation 3x² + 7x + p = 1, find the value of p. Now find the value of k so that the roots of the equation x² + k(4x + k - 1) + p = 0 are equal.

Mathematics

Solve : (x/x + 2)^2 - 7(x/x + 2) + 12 = 0; x ≠ -2.

Quadratic Equations

Related Questions

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

If -2 is a root of the equation 3x2 + 7x + p = 1, find the value of p. Now find the value of k so that the roots of the equation x2 + k(4x + k - 1) + p = 0 are equal.

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

If -2 is a root of the equation 3x² + 7x + p = 1, find the value of p. Now find the value of k so that the roots of the equation x² + k(4x + k - 1) + p = 0 are equal.