You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Roots of a Quadratic Equation

Find the solu...

Question

Find the solution of the equation: $x^{4} - 4 x^{3} + 5 x^{2} - 4 x + 4 = 0.$

(x - 2)^{2} (x - i) (x + i)

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

(x - 2)^{2} (x^{2} + 1)

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

(x + 2)^{2} (x - i) (x + i)

No worries! We‘ve got your back. Try BYJU‘S free classes today!

(x + 2)^{2} (x^{2} + 1)

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct options are
A $(x - 2)^{2} (x^{2} + 1)$
D $(x - 2)^{2} (x - i) (x + i)$
$x^{4} - 4 x^{3} + 5 x^{2} - 4 x + 4 = 0 x^{4} - 4 x^{3} + 4 x^{2} + x^{2} - 4 x + 4 = 0 x^{2} (x^{2} - 4 x + 4) + 1 (x^{2} - 4 x + 4) = 0 (x^{2} + 1) (x^{2} - 4 x + 4) = 0 (x^{2} + 1) (x - 2)^{2} = 0 o r (x + i) (x - i) (x - 2)^{2} = 0$

Suggest Corrections

Similar questions

Q. Prove that

x^{4} + 4

(x + 1 + i) (x + 1 - i) (x - 1 + i) (x - 1 - i) .

Prove that (x+1)(x+1-i)(x-1+i)(x-1-i)=x⁴+4

Solve the following quadratic equations :

(i) $x^{2} - (3 \sqrt{2} + 2 i) x + 6 \sqrt{2} i = 0$

(ii) $x^{2} - (5 - i) x + (18 + i) = 0$

(iii) $(2 + i) x^{2} - (5 - i) x + 2 (1 - i) = 0$

(iv) $x^{2} - (2 + i) x - (1 - 7 i) = 0$

(v) $i x^{2} - 4 x - 4 i = 0$

(vi) $x^{2} + 4 i x - 4 = 0$

(vii) $2 x^{2} + \sqrt{15} i x - i = 0$

(viii) $x^{2} - x + (1 + i) = 0$

(ix) $i x^{2} - x + 12 i = 0$

(x) $x^{2} - (3 \sqrt{2} - 2 i) x - \sqrt{2} i = 0$

(xi) $x^{2} - (\sqrt{2} + i) x + \sqrt{2} i = 0$

(xii) $2 x^{2} - (3 + 7 i) x + (9 i - 3) = 0$

Q. Solve the following quadratic equations:
(i)

x^{2} - (3 \sqrt{2} + 2 i) x + 6 \sqrt{2 i} = 0

(ii)

x^{2} - (5 - i) x + (18 + i) = 0

(iii)

(2 + i) x^{2} - (5 - i) x + 2 (1 - i) = 0

(iv)

x^{2} - (2 + i) x - (1 - 7 i) = 0

(v)

i x^{2} - 4 x - 4 i = 0

(vi)

x^{2} + 4 i x - 4 = 0

(vii)

2 x^{2} + \sqrt{15} i x - i = 0

(viii)

x^{2} - x + (1 + i) = 0

(ix)

i x^{2} - x + 12 i = 0

(x)

x^{2} - (3 \sqrt{2} - 2 i) x - \sqrt{2} i = 0

(xi)

x^{2} - (\sqrt{2} + i) x + \sqrt{2} i = 0

(xii)

2 x^{2} - (3 + 7 i) x + (9 i - 3) = 0

Q. If

x = 1 + i

is a root of the equation

x^{3} - i x + 1 - i = 0

, then the other real root is

Join BYJU'S Learning Program

Find the solution of the equation: x4−4x3+5x2−4x+4=0.

The correct options are A (x−2)2(x2+1) D (x−2)2(x−i)(x+i) x4−4x3+5x2−4x+4=0x4−4x3+4x2+x2−4x+4=0x2(x2−4x+4)+1(x2−4x+4)=0(x2+1)(x2−4x+4)=0(x2+1)(x−2)2=0or(x+i)(x−i)(x−2)2=0

Find the solution of the equation: $x^{4} - 4 x^{3} + 5 x^{2} - 4 x + 4 = 0.$