Solve : x 4 - 10x 2 + 9 = 0

Let x 2 = y, ⇒ x 4 - 10x 2 + 9 = 0 ⇒ y 2 - 10y + 9 = 0 ⇒ y 2 - 9y - y + 9 = 0 ⇒ y(y - 9) - 1(y - 9) = 0 ⇒ (y - 1)(y - 9) = 0 ⇒ y - 1 = 0 or y - 9 = 0 [Zero product rule] ⇒ y = 1 or y = 9. ∴ x 2 = 1 or x 2 = 9 ⇒ x = or x = Hence, x = +3, -3, +1, -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 :
x⁴ - 10x² + 9 = 0

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 :x4 - 10x2 + 9 = 0

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 :
x⁴ - 10x² + 9 = 0

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.