Page 44 - Mathematics Class - XI

Viva-Voce

1. What is a quadratic equation?
Ans. A quadratic equation is an equation of the form ax + bx + c = 0, a ≠ 0 where a, b, c are numbers
2
(real or complex) and x is a variable.
2. What is meant by the roots of a quadratic equation?
Ans. The values of the variable which satisfy the given quadratic equation are called roots of the quadratic
equation.

3. Can a quadratic equation have more than two roots?
Ans. No, every quadratic equation has two and only two roots.
4. Solve the quadratic equation: x + 1 = 0.
2
Ans. x + 1 = 0 ⇒ x = –1, i.e., x = ± −1 = ± i
2
2
5. State the fundamental theorem of algebra.
Ans. Every polynomial equation f(x) = 0 of degree n has exactly n roots (real or imaginary).

MCQs

1. The roots of equation x – 1 = 0
4
a) 1, 1, i, –i b) 1, –1, i, –i c) 1, –1, w, –w d) None of these
2

2
2. If Z 3 i 5 , then the locus of Z is
a) circle b) line c) parabola d) None of these
3. The roots of the equation 16x + 49 = 0 are
2

a) 7i − 7i b) 4i − 4i c) 7, –4 d) None of these
,
,
4 4 7 7
1 1
4. If a, b are the roots of the equation x – ax + b = 0 then the value of is
2

b b 2 1 b + 2 b 2 + 1 b − 2 b 2 −
2
a) b) c) 1 d) None of these
b b b
5. If 2x = –1 + 3i , then (1 – x + x) – (1 – x + x ) is equal to
2 6
2
6
a) 32 b) –64 c) 64 d) 0
Answers: 1. b) 1, –1, i, –i 2. a) circle 3. a) 7i − 7i
,
4 4
b + 2 b 2 + 1
4. b) 5. d) 0
b

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