Question

If one root of equation x^2+ax+3=0 is 1, then what is its other root ?

Answer 1

Answer :

• Other root = 3

• a = -4

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 + C = 0 , then ;

• Sum of roots , (α + ß) = -b/a

• Product of roots , (αß) = c/a

★ If α and ß are the roots of a quadratic equation , then that quadratic equation is given as : k•[ x² - (α + ß)x + αß ] = 0 , k ≠ 0.

Answer :

Here ,

The given quadratic equation is ;

x² + ax + 3 = 0 .

Now ,

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

A = 1

B = a

C = 3

Let α = 1 (given) and ß be the roots of the given quadratic equation .

Thus ,

The product of roots of the given quadratic equation will be given as ;

=> αß = C/A

=> 1•ß = 3/1

=> ß = 3

Also ,

The sum of roots of the given quadratic equation will be given as ;

=> α + ß = -B/A

=> 1 + 3 = -a/1

=> 4 = -a

=> a = -4

Hence ,

• Other root of the given quadratic equation is 3 .

• Moreover , the value of a will be -4 .