Question

Answer the attached question no. 14​

Answer 1

Answer :

c = b²/4a

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.

★ The discriminant , D of the quadratic equation ax² + bx + c = 0 is given by ;

D = b² - 4ac

★ If D = 0 , then the roots are real and equal .

★ If D > 0 , then the roots are real and distinct .

★ If D < 0 , then the roots are unreal (imaginary) .

Solution :

Here ,

The given quadratic equation is ;

ax² + bx + c = 0 .

Also ,

The discriminant of the given quadratic equation will be given as ;

D = b² - 4ac

For real and equal roots , the discriminant of the given quadratic equation must be zero .

Thus ,

=> D = 0

=> b² - 4ac = 0

=> b² = 4ac

=> c = b²/4a

Hence c = b²/4a .