Answer the attached question no. 14
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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 .