Question

find the value of discriminant
${x }^{2} + 7x - 1 = 0$
​

Answer 1

Answer:

${x}^{2} + 7x - 1 = 0 \\ \\ here \: a \: = 1 \\ \\ b \: = 7 \\ \\ c = - 1 \\ \\ we \: know \: \\ \\ discriminant = {b}^{2} - 4ac \\ \\ = {(7)}^{2} - 4 \times 1 \times ( - 1) \\ \\ = 9 - 4 \times ( - 1) \\ \\ = 9 - ( - 4) \\ \\ = 9 + 4 \\ \\ = 13$

hope this much helps uh ❣️

Answer 2

Answer :

D = 53

Note :

★ 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 :

• Given : x² + 7x - 1 = 0
• To find : Discriminant , D = ?

Here ,

The given quadratic equation is :

x² + 7x - 1 = 0

Now ,

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

a = 1

b = 7

c = -1

Now ,

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

=> D = b² - 4ac

=> D = 7² - 4•1•(-1)

=> D = 49 + 4

=> D = 53

Hence ,

Discriminant , D = 53

Moreover ,

The discriminant D > 0 , hence the given quadratic equation will have real and distinct roots .