Question

Question 7
If the difference between the roots of the equation x2 + ax+8 = 0) is 2, then the value
will be
(a)a= 8
(b) a = +6
(c) a= +7
(d) a = +9
​

Answer 1

Answer :

Option (b) : a =6

Note:

★ The possible values of the variable which satisfy the equation are called its roots or solutions .

★ A quadratic equation can have atmost two roots .

★ The general form of a quadratic equation is given as ; Ax² + Bx + C = 0

★ If α and ß are the roots of the quadratic equation Ax² + Bx + B = 0 , then ;

• Sum of roots , (α + ß) = -B/A

• Product of roots , (αß) = C/A

Solution :

Here ,

The given quadratic equation is ;

x² + ax + 8 = 0 .

Now ,

Comparing the given quadratic equation with the general quadratic equation Ax² + Bx + C = 0 , we have ;

A = 1

B = a

C = 8

Now ,

Let α and ß be the roots of the given quadratic equation such that α > ß .

Thus ,

=> Sum of roots = -B/A

=> α + ß = -a/1

=> α + ß = -a

Also ,

=> Product of roots = C/A

=> αß = 8/1

=> αß = 8

Also ,

It is given that , the difference between the roots is 2 .

Thus ,

α - ß = 2

Now ,

We know that ,

=> (α + ß)² = (α - ß)² + 4αß

=> (-a)² = 2² + 4•8

=> a² = 4 + 32

=> a² = 36

=> a = √36

=> a = 6

Hence , a = 6 .