Question

Determine the nature of roots of 2y2 + 11y – 7 = 0 plz tell the ans if any one is smart​

Answer 1

Answer:

For nature of roots,

we have to find the discriminant

$discriminant \: = {b}^{2} - 4ac \\ = {11}^{2} - 4 \times 2 \times ( - 7) \\ = 121 + 56 \\ = 177$

since discriminant > 0

therefore the roots of the given quadratic equation are real and distinct.

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

★ 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 in variable y is ; 2y² + 11y - 7 = 0 .

Now ,

Comparing the given quadratic equation with the general quadratic equation ay² + by + c = 0 , we have ;

a = 2

b = 11

c = -7

Now ,

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

=> D = b² - 4ac

=> D = 11² - 4•2•(-7)

=> D = 121 + 56

=> D = 177

=> D > 0

Clearly ,

The discriminant of the given quadratic equation is greater than zero , thus its roots will be real and distinct .