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Chapter 8 Quadratic Equations R.D. Sharma Solutions for Class 10th Math Exercise 8.1

1. Which of the following are quadratic equations ?

Solution


2. In each of the following , determine whether the given values are solutions of the given equation or not :

Solution

(i)

(ii) 

(iii)

(iv)

(v)

(vi)

(vii)

3. In each of the following , find the value of k for which the given value is a solution of the given equation :

Solution

(i)

(ii) 

(iii) 

(iv) 

 4. Determine if, 3 is a root of the equation given below:

Solution


5. If x = 2/3 and x = -3 are the roots of the equation ax2 + 7x + b = 0, find the values of a and b .   

Solution

We know that x = -2/3 and x = -3 are the roots of the equation ax2 + 7x + b. When we the value of x in this equation, we will get the result as 0.
Putting x = -2/3
a(2/3)2 + 7(2/3) + b = 0
⇒ 4/9 a +14/3 + b =0
⇒ 4/9 a  + b = -14/3 --- (i)

Putting x = -3
a(-3)2 + 7(-3) + b = 0
⇒ 9a - 21 + b =0
⇒ 9a  + b = 21 --- (ii)

Subtracting (i)  from (ii), we get
9a  + b - (4/9 a  + b) = 21 + 14/3
⇒ 9a  + b - 4/9 a  -b = 77/3
⇒ 77/9 a = 49/3
⇒  a = 77/3 × 9/77
⇒  a = 3

Now, putting a =3 in equation (ii),
9×3 + b = 21
⇒ 27 + b = 21
⇒  b = 21 - 27
⇒  b = -6

Thus, a = 3 and b = -6

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