Which of the following is the root of quadratic equation nbsp- -x-1-a-2-b-2 -0-b-a-b-1-ab-1-a-ab nbsp-

The correct option is B b 1/aGiven Quadratic equation is (x+1/a)^2 b^2 =0 ⇒ (x+1/a)^2 =b^2 ⇒ (x+1/a)= ± b ⇒ x =± b 1/a ⇒ Roots of the qudratic equation are ...

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Standard X

Mathematics

Roots of Quadratic equation

Which of the ...

Question

Which of the following is the root of quadratic equation $(x + \frac{1}{a})^{2} - b^{2} = 0$ ?

\frac{- b}{a}

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- a b

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- b - \frac{1}{a}

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b + \frac{1}{a}

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Solution

The correct option is C $- b - \frac{1}{a}$
Given Quadratic equation is $(x + \frac{1}{a})^{2} - b^{2} = 0 \Rightarrow (x + \frac{1}{a})^{2} = b^{2} \Rightarrow (x + \frac{1}{a}) = \pm b \Rightarrow x = \pm b - \frac{1}{a}$

$\Rightarrow$ Roots of the qudratic equation are $- b - \frac{1}{a}$ and $b - \frac{1}{a}$

$∴$ Among the given options, root of the quadratic equation is $- b - \frac{1}{a}$ .

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Similar questions

Q. Which of the following is the root of quadratic equation

(x + \frac{1}{a})^{2} - b^{2} = 0

Q. Which of the following is a root of the quadratic equation

(x + \frac{1}{a})^{2} - b^{2} = 0

Q. If

a

and

b

are the roots of the quadratic equation

x^{2} - 4 x + 3 = 0

, then

(1 + a + a^{2} + a^{3} . . .) (1 + b + b^{2} + b^{3} + . . . .)

equal to

Q. If the roots of the quadratic equation

k x^{2} + (a + b) x + a b = 0

are

(- 1, - b)

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Q. Which step in the following problem is wrong?

a = b = 1

a = b

step-1:

a^{2} = a b

step-2:

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

step-3:

(a + b) (a - b) = b (a - b)

step-4: a + b =

\frac{b (a - b)}{a - b}

a + b = b

1 + 1 = 1

2 = 1

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Which of the following is the root of quadratic equation (x+1a)2−b2=0?

The correct option is C −b−1aGiven Quadratic equation is (x+1a)2−b2=0⇒(x+1a)2=b2⇒(x+1a)=±b⇒x=±b−1a ⇒ Roots of the qudratic equation are −b−1a and b−1a ∴ Among the given options, root of the quadratic equation is −b−1a.

Which of the following is the root of quadratic equation $(x + \frac{1}{a})^{2} - b^{2} = 0$ ?