give ncert exemplar class 10 ch 4 important questions
Answers
Answer:
NCERT Exemplar Problems Class 10 Maths Solutions Chapter 4 Quadratic Equations
Exercise 4.1 Multiple Choice Questions (MCQs)
Question 1:
Which of the following is a quadratic equation?
(a) x2 + 2x + 1 = (4 – x)2 + 3
(b) – 2x2 = (5 – x) (2x – \frac { 2 }{ 5 }
(c) (k + 1)x2 + – \frac { 3 }{ 2 } x = 7, where k = -1
(d) x3 – x2 =(x -1)3
Solution:
ncert-exemplar-problems-class-10-maths-quadratic-equations-Ex-4.1-1s-1
ncert-exemplar-problems-class-10-maths-quadratic-equations-Ex-4.1-1s-2
Question 2:
Which of the following is not a quadratic equation?
(a) 2 (x -1)2 = 4x2 – 2x +1
(b) 2x – x2 = x2 + 5
(c) (-√2X +√3)2 = 3x2 – 5x
(d) (x2 + 2x)2 = x4 + 3 + 4x2
Solution:
ncert-exemplar-problems-class-10-maths-quadratic-equations-Ex-4.1-2s
Question 3:
Which of the following equations has 2 as a root?
(a) x2-4x + 5=0
(b) x2 + 3x-12 =0
(c) 2x2 – 7x + 6 = 0
(d) 3x2 – 6x – 2 = 0
Solution:
ncert-exemplar-problems-class-10-maths-quadratic-equations-Ex-4.1-3s
Question 4:
If \frac { 1 }{ 2 } is a root of the equation x2 + kx –\frac { 5 }{ 4 } = 0, then the value of k is
(a) 2 (b) -2 (c) \frac { 1 }{ 4 } (d)\frac { 1 }{ 2 }
Solution:
ncert-exemplar-problems-class-10-maths-quadratic-equations-Ex-4.1-4s
Question 5:
Which of the following equations has the sum of its roots as 3?
(a) 2x2 – 3x + 6 = 0
(b) -x2 + 3x – 3 = 0
(c) √2x2 – \frac { 3 }{ \sqrt { 2 }}x + 1 = 0
(d) 3x2 – 3x + 3 = 0
Solution:
ncert-exemplar-problems-class-10-maths-quadratic-equations-Ex-4.1-5s-1
ncert-exemplar-problems-class-10-maths-quadratic-equations-Ex-4.1-5s-2
Question 6:
Value(s) of k for which the quadratic equation 2x2 -kx + k = 0 has equal roots is/are
(a) 0 (b) 4 (c) 8 (d) 0, 8
Solution:
(d)
Given equation is 2x2 – kx + k- 0
On comparing with ax2 + bx + c = 0, we get
a = 2, b= – k and c = k
For equal roots, the discriminant must be zero.
ncert-exemplar-problems-class-10-maths-quadratic-equations-Ex-4.1-6s
Hence, the required values of k are 0 and 8.
Question 7:
Which constant must be added and subtracted to solve the quadratic
equation 9x2 +\frac { 3 }{ 4 } x – √2= 0 by the method of completing the square?
(a) \frac { 1 }{ 8 } (b) \frac { 1 }{ 64 } (c) \frac { 1 }{ 4 } (d) \frac { 9 }{ 64 }
Solution:
ncert-exemplar-problems-class-10-maths-quadratic-equations-Ex-4.1-7s
Question 8:
The quadratic equation 2x2 – √5x + 1 = 0 has
(a) two distinct real roots
(b) two equal real roots
(c) no real roots
(d) more than 2 real roots
Solution:
ncert-exemplar-problems-class-10-maths-quadratic-equations-Ex-4.1-8s
Question 9:
Which of the following equations has two distinct real roots?
(a)2x2-3√2x +\frac { 9 }{ 4 } =0
(b) x2 + x – 5 =0
(c) x2 + 3x + 2√2 =0
(d)5x2-3x + 1=0
Solution:
ncert-exemplar-problems-class-10-maths-quadratic-equations-Ex-4.1-9s
ncert-exemplar-problems-class-10-maths-quadratic-equations-Ex-4.1-9s-1
Question 10:
Which of the following equations has no real roots?
(a) x2 – 4x + 3√2 =0
(b)x2+4x-3√2=0
(c) x2 – 4x – 3√2 = 0
(d) 3x2 + 4√3x + 4=0
Solution:
ncert-exemplar-problems-class-10-maths-quadratic-equations-Ex-4.1-10s-1
ncert-exemplar-problems-class-10-maths-quadratic-equations-Ex-4.1-10s-2
Question 11:
(x2 +1)2 – x2 = 0 has
(a) four real roots
(b) two real roots
(c) no real roots
(d) one real root
Solution:
ncert-exemplar-problems-class-10-maths-quadratic-equations-Ex-4.1-11s
Exercise 4.2 Very Short Answer Type Questions
Question 1:
State whether the following quadratic equations have two distinct real roots. Justify your answer.
ncert-exemplar-problems-class-10-maths-quadratic-equations-Ex-4.2-1Q
Solution:
ncert-exemplar-problems-class-10-maths-quadratic-equations-Ex-4.2-1s-1
ncert-exemplar-problems-class-10-maths-quadratic-equations-Ex-4.2-1s-2
ncert-exemplar-problems-class-10-maths-quadratic-equations-Ex-4.2-1s-3
ncert-exemplar-problems-class-10-maths-quadratic-equations-Ex-4.2-1s-4
Question 2:
Write whether the following statements are true or false. Justify your answers.
(i) Every quadratic equation has exactly one root.
(ii) Every quadratic equation has atleast one real root.
(iii) Every quadratic equation has atleast two roots.
(iv) Every quadratic equation has atmost two roots.
(v) If the coefficient of x2 and the constant term of a quadratic equation have opposite
signs, then the quadratic equation has real roots.
(vi) If the coefficient of x2 and the constant term have the same sign and if the coefficient of x term is zero, then the quadratic equation has no real roots.
Solution:
(i) False, since a quadratic equation has two and only two roots.
(ii) False, for example x2 + 4 = O has no real root.
(iii) False, since a quadratic equation has two and only two roots.
(vi) True, because every quadratic polynomial has atmost two roots.
(v) True, since in this case discriminant is always positive, so it has always real roots, e., ac < 0 and so, b2 – 4ac > 0.
(vi) True, since in this case discriminant is always negative, so it has no real roots e., if b = 0, then b2 – 4ac ⇒ – 4ac < 0and ac>0.