CBSE Class 10 Maths Chapter 4 Quadratic Equations for Important Questions with Solutions

CBSE Class 10 Maths Chapter 4 Important Question With Solutions

Class 10 Maths Chapter 4 Quadratic Equations is a part of the second unit Algebra which has a total weightage of 20 marks.  Student can download in PDF format end page given links.

The prescribed topics to be covered under Quadratic equations are: Standard form of a quadratic equation ax2 + bx + c = 0, (a ≠ 0). Solutions of quadratic equations (only real roots) by factorization, and by using quadratic formula. Relationship between discriminant and nature of roots.

MULTIPLE CHOICE QUESTIONS ( 1 MARK)

Q1. What is the positive root of √3x²+6 = 9
(a) 3
(b) 5
(c) 0
(d) none of these

Ans:(b) 5
Q2. For what value(s) of a quadratic equation 3ax²-6x + 1 = 0 has no real roots?
(a) a > 3
(b) a <3
(c) a =3
(d) none

Ans:(a) a > 3
Q3.Find the nature of the roots of the Quadratic equation 2x² – 4x + 3 = 0 ?
(a) real roots
(b) no real roots
(c) equal roots
(d) none

Ans:(b) no real roots
Q4.Find the positive values of k for which the Quadratic equation x² + kx + 64 = 0 and
x² – 8x + k = 0, both will have the real roots?
(a) k=4
(b) k=16
(c) k> 16
(d) k< 4

Ans:(b) k=16
Q5. If the sum of the roots of the quadratic equation 3x² + (2k + 1)x – (k + 5) = 0 is equal to the
product of roots, then the value of k is
(a) 2
(b) 3
(c) 4
(d) 5

Ans:(c) 4

SHORT ANSWER TYPE QUESTIONS (2 MARKS)

Q1.For what value of p for equation 2x² + 3x + p = 0 will have real roots?

Q2. Find the sum of the roots of the quadratic equation3x² – 9x+5=0?

Q3. If is a root of the equation x² + kx-5=0, then what is the value of k?

Q4. If the one root of the equation 4x² – 2x + p − 4 =0 be the reciprocal of other, then
what is the value of p?

Q5. What is the value of k for which the quadratic equation2x² – kx + k =0 has equal
roots?

SHORT ANSWER TYPE QUESTIONS (3 MARKS)

Q1. Find the nature of the roots of the following quadratic equations. If the real roots
exist, find them: 2x²+4x-8=0

Q2. Using the quadratic formula, solve the following quadratic equation for x. p²x² +
(p² – q²)x-q² = 0

Q3. If a and ẞ are the roots of the equation 2x²-6x + a = 0 and 2a+ 5ẞ = 12, find the
value of a?
Q4. If-5 is a root of the quadratic equation 2x² + px – 15 = 0 and the quadratic equation
p(x² + x) + k = 0 has equal roots, then find the value of k.
Q5. Find the positive value of k for which the equation x²+kx+64 = 0 and x²-8x+k=0
will both have real roots?

LONG ANSWER TYPE QUESTIONS (4 MARKS)

Q1. Seven years ago, Rahul’s age was five times the square of Reena’s age. Three years
hence, Reena’s age will be two fifth of Rahul’s age. Find their present ages.
Q2. The diagonal of a rectangular field is 16metres more than the shorter side. If the
longer side is 14 metres more than the shorter side, then find the length of the sides of
the field.
Q3. One fourth of a herd of camel was seen in the forest. Twice the square root of the
herd had gone to the mountains and the remaining 15 camels were seen on the bank
of the river. Find the total number of camels.

CBSE Class 10 Maths Chapter 4 Quadratic Equations for Important Questions with Solutions Download PDF