## ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 5 Quadratic Equations in One Variable Ex 5.1

ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 5 Quadratic Equations in One Variable Ex 5.1

Question 1.

Check whether the following are quadratic equations:

(i) \(\sqrt { 3 } { x }^{ 2 }-2x+\frac { 3 }{ 5 } =0\)

(ii) (2x + 1) (3x – 2) = 6(x + 1) (x – 2)

(iii) \({ (x-3) }^{ 3 }+5={ x }^{ 3 }+7{ x }^{ 2 }-1\)

(iv) \(x-\frac { 3 }{ x } =2,x\neq 0\)

(v) \(x+\frac { 2 }{ x } ={ x }^{ 2 },x\neq 0\)

(vi) \({ x }^{ 2 }+\frac { 1 }{ { x }^{ 2 } } =3,x\neq 0 \)

Solution:

Question 2.

In each of the following, determine whether the given numbers are roots of the given equations or not;

(i) x² – x + 1 = 0; 1, -1

(ii) x² – 5x + 6 = 0; 2, -3

(iii) 3x² – 13x – 10 = 0; 5,\(\\ \frac { -2 }{ 3 } \)

(iv) 6x² – x – 2 = 0; \(\\ \frac { -1 }{ 2 } \), \(\\ \frac { 2 }{ 3 } \)

Solution:

Question 3.

In each of the following, determine whether the given numbers are solutions of the given equation or not:

(i) x² – 3√3x + 6 = 0; √3, -2√3

(ii) x² – √2x – 4 = 0, x = -√2, 2√2

Solution:

Question 4.

(i) If \(– \frac { 1 }{ 2 } \) is a solution of the equation 3x² + 2kx – 3 = 0, find the value of k.

(ii) If \(\\ \frac { 2 }{ 3 } \) is a solution of the equation 7x² + kx – 3 = 0, find the value of k.

Solution:

Question 5.

(i) If √2 is a root of the equation kx² + √2 – 4 = 0, find the value of k.

(ii) If a is a root of the equation x² – (a + b)x + k = 0, find the value of k.

Solution:

Question 6.

If \(\\ \frac { 2 }{ 3 } \) and -3 are the roots of the equation px² + 7x + q = 0, find the values of p and q.

Solution: