If a2-b2-c2-2 andfx- 1-a2 x 1-b2 x 1-c2 x- 1-a2 x 1-b2 x 1-c2 x- 1-a2 x 1-b2 x 1-c2 x -then fx is a polynomial of degree

The correct option is D 2Given, Applying C1→C1 + C2 + C3 and using a2 + b2 + c2 + 2 =0, we get Applying R1→R1 R3, R2 →R2 R3 ⟹f(x) is a polynomial of deg ...

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Standard XII

Mathematics

Properties of Determinants

If a2+b2+c2=-...

Question

If a² +b² + c² =-2 and

then f(x) is a polynomial of degree

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Solution

The correct option is A
2

Given,

Applying C₁→C₁ + C₂ + C₃ and using a² + b²+ c² + 2 =0, we get

Applying R₁→R₁ - R₃, R₂ →R₂ - R₃

_{⟹f(x) is a polynomial of degree 2}

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Similar questions

Q. If

a^{2} + b^{2} + c^{2} = - 2

and

f (x) = ∣ ∣ ∣ ∣ ∣ \begin{matrix} 1 + a^{2} x & (1 + b^{2}) x & (1 + c^{2}) x (1 + a^{2}) x & 1 + b^{2} x & (1 + c^{2}) x (1 + a^{2}) x & (1 + b^{2}) x & 1 + c^{2} x \end{matrix} ∣ ∣ ∣ ∣ ∣

then f(x) is a polynomial of degree

Q. If

a^{2} + b^{2} + c^{2} = - 2

and

f (x) = ∣ ∣ ∣ ∣ ∣ \begin{matrix} {1 + a}^{2} x & {(1 + b}^{2}) x & ({1 + c}^{2}) x ({1 + a}^{2}) x & {1 + b}^{2} x & ({1 + c}^{2}) x ({1 + a}^{2}) x & ({1 + b}^{2}) x & {1 + c}^{2} x \end{matrix} ∣ ∣ ∣ ∣ ∣

, then

f (x)

is a polynomial of degree

Q. If

a^{2} + b^{2} + c^{2} = - 2

, and

A = ⎡ ⎢ ⎢ ⎣ \begin{matrix} 1 + a^{2} x & (1 + b^{2}) x & (1 + c^{2}) x (1 + a^{2}) x & 1 + b^{2} x & (1 + c^{2}) x (1 + a^{2}) x & (1 + b^{2}) x & 1 + c^{2} x \end{matrix} ⎤ ⎥ ⎥ ⎦

, then

A

is non-singular if

x =

Q. If

a^{2} + b^{2} + c^{2} + 2 = 0

and

f (x) = ∣ ∣ ∣ ∣ ∣ \begin{matrix} 1 + a^{2} x & (1 + b^{2}) x & (1 + c^{2}) x (1 + a^{2}) x & 1 + b^{2} x & (1 + c^{2}) x (1 + a^{2}) x & (1 + b^{2}) x & 1 + c^{2} x \end{matrix} ∣ ∣ ∣ ∣ ∣

then

f (x)

is poynomial of degree

Q. If

α

and

β

are the roots of the equation

a x^{2} + b x + c = 0

then the equation whose roots are

(α^{2} + β^{2}), (\frac{1}{α^{2}} + \frac{1}{β^{2}})

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If a2 +b2 + c2 =-2 and then f(x) is a polynomial of degree

The correct option is A 2Given, Applying C1→C1 + C2 + C3 and using a2 + b2 + c2 + 2 =0, we get Applying R1→R1 - R3, R2 →R2 - R3 ⟹f(x) is a polynomial of degree 2

If a² +b² + c² =-2 and

then f(x) is a polynomial of degree

The correct option is A
2

Given,

Applying C₁→C₁ + C₂ + C₃ and using a² + b²+ c² + 2 =0, we get

Applying R₁→R₁ - R₃, R₂ →R₂ - R₃

_{⟹f(x) is a polynomial of degree 2}