If x 4 - 5x 2 + 4 = 0; the values of x are : 1. 1 or 2 2. 1 or 2 3. -1 and 2 4. -2, -1, 1 or 2

Given, ⇒ x 4 - 5x 2 + 4 = 0 ⇒ x 4 - 4x 2 - x 2 + 4 = 0 ⇒ x 2 (x 2 - 4) - 1(x 2 - 4) = 0 ⇒ (x 2 - 1)(x 2 - 4) = 0 ⇒ x 2 - 1 = 0 or x 2 - 4 = 0 ⇒ x 2 = 1 or x 2 = 4 ⇒ x = or x = ⇒ x = 1 or x = 2. Hence, Option 2 is the correct option.

Mathematics

If x⁴ - 5x² + 4 = 0; the values of x are :
1 or 2
± 1 or ± 2
-1 and 2
-2, -1, 1 or 2

Quadratic Equations

23 Likes

Answer

Given,

⇒ x⁴ - 5x² + 4 = 0

⇒ x⁴ - 4x² - x² + 4 = 0

⇒ x²(x² - 4) - 1(x² - 4) = 0

⇒ (x² - 1)(x² - 4) = 0

⇒ x² - 1 = 0 or x² - 4 = 0

⇒ x² = 1 or x² = 4

⇒ x = $\sqrt{1}$ or x = $\sqrt{4}$

⇒ x = ± 1 or x = ± 2.

Hence, Option 2 is the correct option.

Answered By

10 Likes

Mathematics

If x⁴ - 5x² + 4 = 0; the values of x are :
1 or 2
± 1 or ± 2
-1 and 2
-2, -1, 1 or 2

Quadratic Equations

Answer

Related Questions

Find the value of k for which the equation 3x² - 6x + k = 0 has distinct and real roots.

Given that 2 is a root of the equation 3x² - p(x + 1) = 0 and that the equation px² - qx + 9 = 0 has equal roots, find the values of p and q.

For equation $\dfrac{1}{x} + \dfrac{1}{x - 5} = \dfrac{3}{10}$ ; one value of x is :
$-\dfrac{5}{3}$
10
-10
5

Which of the following is correct for the equation $\dfrac{1}{x - 3} - \dfrac{1}{x + 5}$ = 1 ?
x ≠ 3 and x = -5
x = 3 and x ≠ -5
x ≠ 3 and x ≠ -5
x > 3 and x < 5

Mathematics

If x4 - 5x2 + 4 = 0; the values of x are :1 or 2± 1 or ± 2-1 and 2-2, -1, 1 or 2

Quadratic Equations

Answer

Related Questions

Find the value of k for which the equation 3x2 - 6x + k = 0 has distinct and real roots.

Given that 2 is a root of the equation 3x2 - p(x + 1) = 0 and that the equation px2 - qx + 9 = 0 has equal roots, find the values of p and q.

For equation 1x+1x−5=310\dfrac{1}{x} + \dfrac{1}{x - 5} = \dfrac{3}{10}x1​+x−51​=103​; one value of x is :−53-\dfrac{5}{3}−35​10-105

Which of the following is correct for the equation 1x−3−1x+5\dfrac{1}{x - 3} - \dfrac{1}{x + 5}x−31​−x+51​ = 1 ?x ≠ 3 and x = -5x = 3 and x ≠ -5x ≠ 3 and x ≠ -5x > 3 and x < 5

If x⁴ - 5x² + 4 = 0; the values of x are :
1 or 2
± 1 or ± 2
-1 and 2
-2, -1, 1 or 2

Find the value of k for which the equation 3x² - 6x + k = 0 has distinct and real roots.

Given that 2 is a root of the equation 3x² - p(x + 1) = 0 and that the equation px² - qx + 9 = 0 has equal roots, find the values of p and q.

For equation $\dfrac{1}{x} + \dfrac{1}{x - 5} = \dfrac{3}{10}$ ; one value of x is :
$-\dfrac{5}{3}$
10
-10
5

Which of the following is correct for the equation $\dfrac{1}{x - 3} - \dfrac{1}{x + 5}$ = 1 ?
x ≠ 3 and x = -5
x = 3 and x ≠ -5
x ≠ 3 and x ≠ -5
x > 3 and x < 5