Solve x = (3x + 1)/(4x) by factorisation

Given, ⇒ ⇒ x.4x = 3x + 1 ⇒ 4x 2 = 3x + 1 ⇒ 4x 2 - 3x - 1 = 0 ⇒ 4x 2 - 4x + x - 1 = 0 ⇒ 4x(x - 1) + 1(x - 1) = 0 ⇒ (4x + 1)(x - 1) = 0 ⇒ (4x + 1) = 0 or (x - 1) = 0 ⇒ 4x = -1 or x = 1 ⇒ x = or x = 1. Hence, x = or x = 1.

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 = (3x + 1)/(4x) by factorisation

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 = (3x + 1)/(4x) by factorisation

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.