Question

Q5. What will be the nature of roots of quadratic equation x2 + 3x – 12 = 0?​

Answer 1

Step-by-step explanation:

THE NATURE OF ROOTS DEPENDS UPON ITS DISCRIMINATE

SO IN EQUATION

X²+3X-12=0

D=b²-4ac=3²-4×(-12)×1=9+48=57

AS D IS NOT PERFECT SQUARE & D>0

SO, ROOTS ARE REAL AND IRRATIONAL

Answer 2

Answer :

Real and distinct .

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 ;

x² + 3x - 12 = 0 .

Now ,

Comparing the given quadratic equation with the general quadratic equation ax² + bx + c = 0 , we have ;

a = 1

b = 3

c = -12

Now ,

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

=> D = b² - 4ac

=> D = 3³ - 4×1×(-12)

=> D = 9 + 48

=> D = 57

=> D > 0

Clearly ,

The discriminant of the given quadratic equation is greater than zero .

Hence ,

Roots are real and distinct .